Yardım:Matematiksel formüller - Vikipedi
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İçindekiler

  • Giriş
  • 1 Kodlama
  • 2 Sunum
  • 3 TeX ve HTML
    • 3.1 HTML'nin avantajları
    • 3.2 TeX kullanımının avantajları
  • 4 Fonksiyonlar, semboller, özel karakterler
    • 4.1 Aksanlar/Vurgular
    • 4.2 Standart fonksiyonlar
    • 4.3 Modüler aritmatik
    • 4.4 Türevsel karakterler
    • 4.5 Kümeler
    • 4.6 Operatör işaretler
    • 4.7 Mantıksal ifadeler
    • 4.8 Kök alma
    • 4.9 Eşitlik/Denklik/Benzerlik işaretleri
    • 4.10 Geometrik
    • 4.11 Oklar/Bildiri ifadeleri
    • 4.12 Özel
    • 4.13 Unsorted (new stuff)
  • 5 Üslü ifadeler, toplam-çarpım sembolleri, türev, integral
  • 6 Fractions, matrices, multilines
  • 7 Alphabets and typefaces
  • 8 Parenthesizing big expressions, brackets, bars
  • 9 Spacing
  • 10 Align with normal text flow
  • 11 Forced PNG rendering
  • 12 Color
  • 13 Examples
    • 13.1 Quadratic Polynomial
    • 13.2 Quadratic Polynomial (Force PNG Rendering)
    • 13.3 Quadratic Formula
    • 13.4 Tall Parentheses and Fractions
    • 13.5 Integrals
    • 13.6 Summation
    • 13.7 Differential Equation
    • 13.8 Complex numbers
    • 13.9 Limits
    • 13.10 Integral Equation
    • 13.11 Example
    • 13.12 Continuation and cases
    • 13.13 Prefixed subscript
  • 14 Bug reports
  • 15 See also
  • 16 External links

Yardım:Matematiksel formüller

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Vikipedi, özgür ansiklopedi

MediaWiki yazılımı matematiksel ifadelerin biçimlendirilmesinde LaTeX ve AMSLaTeX yazılımlarını içeren TeX yazılımını kullanmaktadır. Bazı matematiksel formüller kişisel tercihlere bağlı olarak PNG, bazıları ise HTML olarak gözükebilir.

Türkçe'ye çevir
Bu sayfanın tamamının ya da bir kısmının Türkçeye çevrilmesi gerekmektedir.
Bu sayfanın tamamı ya da bir kısmı Türkçe dışındaki bir dilde yazılmıştır. Madde, alakalı dilin okuyucuları için oluşturulmuşsa o dildeki Vikipedi'ye aktarılmalıdır. İlgili değişiklikler gerçekleşmezse maddenin tamamının ya da çevrilmemiş kısımların silinmesi sözkonusu olabilecektir. İlgili çalışmayı yapmak üzere bu sayfadan destek alabilirsiniz


Kodlama

[değiştir | kaynağı değiştir]

Matematiksel kodlar <math> ... </math> kodları arasına yazılır. Math markup goes inside <math> ... </math>. The edit toolbar has a button for this.


Tex kodları doğru yazılmadıkları zaman hata uyarısı verirler. Bu nedenle kodları doğru yazdığınızdan emin olmalısınız.


Sunum

[değiştir | kaynağı değiştir]

It should be pointed out that most of these shortcomings have been addressed by Maynard Handley, but have not been released yet.

The alt attribute of the PNG images (the text that is displayed if your browser can't display images; Internet Explorer shows it up in the hover box) is the wikitext that produced them, excluding the <math> and </math>.

Apart from function and operator names, as is customary in mathematics for variables, letters are in italics; digits are not. For other text, (like variable labels) to avoid being rendered in italics like variables, use \mbox or \mathrm. For example, <math>\mbox{abc}</math> gives abc {\displaystyle {\mbox{abc}}} {\displaystyle {\mbox{abc}}}.

TeX ve HTML

[değiştir | kaynağı değiştir]

Before introducing TeX markup for producing special characters, it should be noted that, as this comparison table shows, sometimes similar results can be achieved in HTML (see Help:Special characters).

TeX kodlaması TeX çıktısı HTML kodlaması HTML çıktısı
<math>\alpha\,</math> α {\displaystyle \alpha \,} {\displaystyle \alpha \,} &alpha; α
<math>\sqrt{2}</math> 2 {\displaystyle {\sqrt {2}}} {\displaystyle {\sqrt {2}}} &radic;2 √2
<math>\sqrt{1-e^2}</math> 1 − e 2 {\displaystyle {\sqrt {1-e^{2}}}} {\displaystyle {\sqrt {1-e^{2}}}} &radic;<span style="text-decoration: overline;">1&minus;''e''&sup2;</div> √1−e²


as follows.

HTML'nin avantajları

[değiştir | kaynağı değiştir]
  1. HTML ile yazılan formüller her zaman yazının bütünü gibi durur.
  2. HTML ile yazılan formüllerde, sayfanın arka planı, font türü, internet sunucusunun ayarları aktif olarak çalışır.
  3. HTML kullanarak yazılan formüller sayfa açılım hızını arttırır.


TeX kullanımının avantajları

[değiştir | kaynağı değiştir]
  1. Tex kalite bakımından HTML'den ileri bir yazılımdır.
  2. Tex yazılımında "<math>x</math>" kodlaması matematiksel değişken anlamına gelir. Fakat HTML'de "x" kodlaması herhangi bir anlama gelebilir. Bu yüzden bilgiler daha kolay kaybolabilir.
  3. TeX yazılımı özellikle formül yazımı için tasarlanmıştır. Bu nedenle daha kolay ve daha işlevseldir.
  4. One consequence of point 1 is that TeX can be transformed into HTML, but not vice-versa. This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It's true that the current situation is not ideal, but that's not a good reason to drop information/contents. It's more a reason to help improve the situation.
  5. Diğer önemli husus TeX MathML kodlamasına, bu kodlamayı destekleyen sunucular tarafından çevirlebilmektedir.
  6. TeX komutlarını kullanırken sunucu desteğine ya da diğer teknik desteklere ihtiyaç duymazsınız. Bu kodlamanın işlevselliğini serverler sağlamaktadır. Bu nedenle her türlü sunucuda, rahatlıkla yazıp kullanabileceğiniz bir kodlama türüdür.

Fonksiyonlar, semboller, özel karakterler

[değiştir | kaynağı değiştir]

Aksanlar/Vurgular

\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a} a ´ a ` a ^ a ~ a ˘ {\displaystyle {\acute {a}}{\grave {a}}{\hat {a}}{\tilde {a}}{\breve {a}}\,\!} {\displaystyle {\acute {a}}{\grave {a}}{\hat {a}}{\tilde {a}}{\breve {a}}\,\!}
\check{a} \bar{a} \ddot{a} \dot{a} a ˇ a ¯ a ¨ a ˙ {\displaystyle {\check {a}}{\bar {a}}{\ddot {a}}{\dot {a}}\,\!} {\displaystyle {\check {a}}{\bar {a}}{\ddot {a}}{\dot {a}}\,\!}

Standart fonksiyonlar

\sin a \cos b \tan c sin ⁡ a cos ⁡ b tan ⁡ c {\displaystyle \sin a\cos b\tan c\,\!} {\displaystyle \sin a\cos b\tan c\,\!}
\sec d \csc e \cot f sec ⁡ d csc ⁡ e cot ⁡ f {\displaystyle \sec d\csc e\cot f\,\!} {\displaystyle \sec d\csc e\cot f\,\!}
\arcsin h \arccos i \arctan j arcsin ⁡ h arccos ⁡ i arctan ⁡ j {\displaystyle \arcsin h\arccos i\arctan j\,\!} {\displaystyle \arcsin h\arccos i\arctan j\,\!}
\sinh k \cosh l \tanh m \coth n sinh ⁡ k cosh ⁡ l tanh ⁡ m coth ⁡ n {\displaystyle \sinh k\cosh l\tanh m\coth n\,\!} {\displaystyle \sinh k\cosh l\tanh m\coth n\,\!}
\operatorname{sh}o \operatorname{ch}p \operatorname{th}q sh ⁡ o ch ⁡ p th ⁡ q {\displaystyle \operatorname {sh} o\operatorname {ch} p\operatorname {th} q\,\!} {\displaystyle \operatorname {sh} o\operatorname {ch} p\operatorname {th} q\,\!}
\operatorname{argsh}r \operatorname{argch}s \operatorname{argth}t argsh ⁡ r argch ⁡ s argth ⁡ t {\displaystyle \operatorname {argsh} r\operatorname {argch} s\operatorname {argth} t\,\!} {\displaystyle \operatorname {argsh} r\operatorname {argch} s\operatorname {argth} t\,\!}
\lim u \limsup v \liminf w \min x \max y lim u lim sup v lim inf w min x max y {\displaystyle \lim u\limsup v\liminf w\min x\max y\,\!} {\displaystyle \lim u\limsup v\liminf w\min x\max y\,\!}
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g inf z sup a exp ⁡ b ln ⁡ c lg ⁡ d log ⁡ e log 10 ⁡ f ker ⁡ g {\displaystyle \inf z\sup a\exp b\ln c\lg d\log e\log _{10}f\ker g\,\!} {\displaystyle \inf z\sup a\exp b\ln c\lg d\log e\log _{10}f\ker g\,\!}
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n deg ⁡ h gcd i Pr j det k hom ⁡ l arg ⁡ m dim ⁡ n {\displaystyle \deg h\gcd i\Pr j\det k\hom l\arg m\dim n\,\!} {\displaystyle \deg h\gcd i\Pr j\det k\hom l\arg m\dim n\,\!}

Modüler aritmatik

s_k \equiv 0 \pmod{m} a \bmod b s k ≡ 0 ( mod m ) a mod b {\displaystyle s_{k}\equiv 0{\pmod {m}}a{\bmod {b}}\,\!} {\displaystyle s_{k}\equiv 0{\pmod {m}}a{\bmod {b}}\,\!}

Türevsel karakterler

\nabla \partial x dx \dot x \ddot y ∇ ∂ x d x x ˙ y ¨ {\displaystyle \nabla \partial xdx{\dot {x}}{\ddot {y}}\,\!} {\displaystyle \nabla \partial xdx{\dot {x}}{\ddot {y}}\,\!}

Kümeler

\forall \exists \empty \emptyset \varnothing ∀ ∃ ∅ ∅ ∅ {\displaystyle \forall \exists \emptyset \emptyset \varnothing \,\!} {\displaystyle \forall \exists \emptyset \emptyset \varnothing \,\!}
\in \ni \not \in \notin \subset \subseteq \supset \supseteq ∈∋∉∉⊂⊆⊃⊇ {\displaystyle \in \ni \not \in \notin \subset \subseteq \supset \supseteq \,\!} {\displaystyle \in \ni \not \in \notin \subset \subseteq \supset \supseteq \,\!}
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus ∩ ⋂ ∪ ⋃ ⨄ ∖ ∖ {\displaystyle \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus \,\!} {\displaystyle \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus \,\!}
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup ⊏⊑⊐⊒ ⊓ ⊔ ⨆ {\displaystyle \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup \,\!} {\displaystyle \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup \,\!}

Operatör işaretler

+ \oplus \bigoplus \pm \mp - + ⊕ ⨁ ± ∓ − {\displaystyle +\oplus \bigoplus \pm \mp -\,\!} {\displaystyle +\oplus \bigoplus \pm \mp -\,\!}
\times \otimes \bigotimes \cdot \circ \bullet \bigodot × ⊗ ⨂ ⋅ ∘ ∙ ⨀ {\displaystyle \times \otimes \bigotimes \cdot \circ \bullet \bigodot \,\!} {\displaystyle \times \otimes \bigotimes \cdot \circ \bullet \bigodot \,\!}
\star * / \div \frac{1}{2} ⋆ ∗ / ÷ 1 2 {\displaystyle \star */\div {\frac {1}{2}}\,\!} {\displaystyle \star */\div {\frac {1}{2}}\,\!}

Mantıksal ifadeler

\land \wedge \bigwedge \bar{q} \to p ∧ ∧ ⋀ q ¯ → p {\displaystyle \land \wedge \bigwedge {\bar {q}}\to p\,\!} {\displaystyle \land \wedge \bigwedge {\bar {q}}\to p\,\!}
\lor \vee \bigvee \lnot \neg q \And ∨ ∨ ⋁ ¬ ¬ q & {\displaystyle \lor \vee \bigvee \lnot \neg q\And \,\!} {\displaystyle \lor \vee \bigvee \lnot \neg q\And \,\!}

Kök alma

\sqrt{2} \sqrt[n]{x} 2 x n {\displaystyle {\sqrt {2}}{\sqrt[{n}]{x}}\,\!} {\displaystyle {\sqrt {2}}{\sqrt[{n}]{x}}\,\!}

Eşitlik/Denklik/Benzerlik işaretleri

\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=} ∼≈≃≅ = ˙ = d e f {\displaystyle \sim \approx \simeq \cong {\dot {=}}{\overset {\underset {\mathrm {def} }{}}{=}}\,\!} {\displaystyle \sim \approx \simeq \cong {\dot {=}}{\overset {\underset {\mathrm {def} }{}}{=}}\,\!}
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto ≤<≪≫≥>≡≢≠ or ≠∝ {\displaystyle \leq <\ll \gg \geq >\equiv \not \equiv \neq {\mbox{or}}\neq \propto \,\!} {\displaystyle \leq <\ll \gg \geq >\equiv \not \equiv \neq {\mbox{or}}\neq \propto \,\!}

Geometrik

\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ ◊ ◻ △ ∠ ⊥ ∣ ∤ ‖ 45 ∘ {\displaystyle \Diamond \,\Box \,\triangle \,\angle \perp \,\mid \;\nmid \,\|45^{\circ }\,\!} {\displaystyle \Diamond \,\Box \,\triangle \,\angle \perp \,\mid \;\nmid \,\|45^{\circ }\,\!}

Oklar/Bildiri ifadeleri

\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow ←←→→↛↔⟵⟶ {\displaystyle \leftarrow \gets \rightarrow \to \not \to \leftrightarrow \longleftarrow \longrightarrow \,\!} {\displaystyle \leftarrow \gets \rightarrow \to \not \to \leftrightarrow \longleftarrow \longrightarrow \,\!}
\mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow ↦⟼↪↩↗↘↙↖ {\displaystyle \mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow \,\!} {\displaystyle \mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow \,\!}
\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft ↑↓↕⇀⇁↼↽↿ {\displaystyle \uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \,\!} {\displaystyle \uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \,\!}
\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow ↾⇃⇂ ⇌ ⇐⇒⇔⟸ {\displaystyle \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \,\!} {\displaystyle \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \,\!}
\Longrightarrow \Longleftrightarrow (or \iff) \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft ⟹⟺⇑⇓⇕⇇⇆⇚↢↫ {\displaystyle \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\!} {\displaystyle \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\!}
\leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright ⇋↶↺↰⇈⇉⇄⇛↣↬ {\displaystyle \leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright \,\!} {\displaystyle \leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright \,\!}
\curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow ↷↻↱⇊⊸↭⇝⇍↮⇏ {\displaystyle \curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow \,\!} {\displaystyle \curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow \,\!}
\nLeftrightarrow \longleftrightarrow ⇎⟷ {\displaystyle \nLeftrightarrow \longleftrightarrow \,\!} {\displaystyle \nLeftrightarrow \longleftrightarrow \,\!}

Özel

\eth \S \P \% \dagger \ddagger \ldots \cdots ð § ¶ % † ‡ … ⋯ {\displaystyle \eth \S \P \%\dagger \ddagger \ldots \cdots \,\!} {\displaystyle \eth \S \P \%\dagger \ddagger \ldots \cdots \,\!}
\smile \frown \wr \triangleleft \triangleright \infty \bot \top ⌣⌢ ≀ ◃ ▹ ∞ ⊥ ⊤ {\displaystyle \smile \frown \wr \triangleleft \triangleright \infty \bot \top \,\!} {\displaystyle \smile \frown \wr \triangleleft \triangleright \infty \bot \top \,\!}
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar ⊢⊨⊩⊨ ‖ ‖ ı ℏ {\displaystyle \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar \,\!} {\displaystyle \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar \,\!}
\ell \mho \Finv \Re \Im \wp \complement \diamondsuit ℓ ℧ Ⅎ ℜ ℑ ℘ ∁ ♢ {\displaystyle \ell \mho \Finv \Re \Im \wp \complement \diamondsuit \,\!} {\displaystyle \ell \mho \Finv \Re \Im \wp \complement \diamondsuit \,\!}
\heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp ♡ ♣ ♠ ⅁ ♭ ♮ ♯ {\displaystyle \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp \,\!} {\displaystyle \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp \,\!}

Unsorted (new stuff)

\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown △ ▽ ◊ Ⓢ ∡ ∄ k ‵ ▴ ▾ {\displaystyle \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown } {\displaystyle \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown }
\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge ◼ ⧫ ★ ∢ ╱ ╲ ∔ ⋒ ⋓ ⊼ {\displaystyle \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge } {\displaystyle \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge }
\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes ⊻ ⩞ ⊟ ⊠ ⊡ ⊞ ⋇ ⋉ ⋊ ⋋ {\displaystyle \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes } {\displaystyle \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes }
\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant ⋌ ⋏ ⋎ ⊝ ⊛ ⊚ ⋅ ⊺ ≦⩽ {\displaystyle \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant } {\displaystyle \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant }
\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq ⪕⪅≊⋖⋘≶⋚⪋≑≓ {\displaystyle \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq } {\displaystyle \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq }
\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft ≒∽⋍⫅⋐≼⋞≾⪷⊲ {\displaystyle \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft } {\displaystyle \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft }
\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot ⊪≏≎≧⩾⪖≳⪆≂⋗ {\displaystyle \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot } {\displaystyle \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot }
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq ⋙≷⋛⪌≖≗≜ ∼≈ ⫆ {\displaystyle \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq } {\displaystyle \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq }
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork ⋑≽⋟≿⪸⊳ ∣∥ ≬⋔ {\displaystyle \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork } {\displaystyle \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork }
\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq ∝ ◂ ∴∍ ▸ ∵ ⪇≰ ⪇≨ {\displaystyle \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq } {\displaystyle \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq }
\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid ≨ ⋦⪉⊀ ⋠ ⪵⋨⪹≁ ∤ {\displaystyle \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid } {\displaystyle \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid }
\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr ⊬⊮⋪⋬⊈ ⊈⊊ ⫋ ⫋ ≯ {\displaystyle \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr } {\displaystyle \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr }
\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq ⪈≱ ⪈≩ ≩ ⋧⪊⊁ ⋡ ⪶ {\displaystyle \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq } {\displaystyle \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq }
\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq ⋩⪺≆ ∦ ∦⊭⊯⋫⋭⊉ {\displaystyle \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq } {\displaystyle \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq }
\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq ⊉⊋ ⫌ ⫌ {\displaystyle \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq } {\displaystyle \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq }
\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus ȷ √ ∗ ⊎ ⋄ △ ▽ ⊖ {\displaystyle \jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus \,\!} {\displaystyle \jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus \,\!}
\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq ⊘ ⊙ ◯ ⨿ ≺≻⪯⪰ {\displaystyle \oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq \,\!} {\displaystyle \oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq \,\!}
\dashv \asymp \doteq \parallel ⊣≍≐ ∥ {\displaystyle \dashv \asymp \doteq \parallel \,\!} {\displaystyle \dashv \asymp \doteq \parallel \,\!}

Üslü ifadeler, toplam-çarpım sembolleri, türev, integral

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Feature Syntax How it looks rendered
HTML PNG
Superscript a^2 a 2 {\displaystyle a^{2}} {\displaystyle a^{2}} a 2 {\displaystyle a^{2}\,\!} {\displaystyle a^{2}\,\!}
Subscript a_2 a 2 {\displaystyle a_{2}} {\displaystyle a_{2}} a 2 {\displaystyle a_{2}\,\!} {\displaystyle a_{2}\,\!}
Grouping a^{2+2} a 2 + 2 {\displaystyle a^{2+2}} {\displaystyle a^{2+2}} a 2 + 2 {\displaystyle a^{2+2}\,\!} {\displaystyle a^{2+2}\,\!}
a_{i,j} a i , j {\displaystyle a_{i,j}} {\displaystyle a_{i,j}} a i , j {\displaystyle a_{i,j}\,\!} {\displaystyle a_{i,j}\,\!}
Combining sub & super x_2^3 x 2 3 {\displaystyle x_{2}^{3}} {\displaystyle x_{2}^{3}}
Preceding and/or Additional sub & super \sideset{_1^2}{_3^4}\prod_a^b ∏ 1 2 ∏ 3 4 a b {\displaystyle \sideset {_{1}^{2}}{_{3}^{4}}\prod _{a}^{b}} {\displaystyle \sideset {_{1}^{2}}{_{3}^{4}}\prod _{a}^{b}}
{}_1^2\!\Omega_3^4 1 2 Ω 3 4 {\displaystyle {}_{1}^{2}\!\Omega _{3}^{4}} {\displaystyle {}_{1}^{2}\!\Omega _{3}^{4}}
Stacking \overset{\alpha}{\omega} ω α {\displaystyle {\overset {\alpha }{\omega }}} {\displaystyle {\overset {\alpha }{\omega }}}
\underset{\alpha}{\omega} ω α {\displaystyle {\underset {\alpha }{\omega }}} {\displaystyle {\underset {\alpha }{\omega }}}
\overset{\alpha}{\underset{\gamma}{\omega}} ω γ α {\displaystyle {\overset {\alpha }{\underset {\gamma }{\omega }}}} {\displaystyle {\overset {\alpha }{\underset {\gamma }{\omega }}}}
\stackrel{\alpha}{\omega} ω α {\displaystyle {\stackrel {\alpha }{\omega }}} {\displaystyle {\stackrel {\alpha }{\omega }}}
Derivative (forced PNG) x', y, f', f\!   x ′ , y ″ , f ′ , f ″ {\displaystyle x',y'',f',f''\!} {\displaystyle x',y'',f',f''\!}
Derivative (f in italics may overlap primes in HTML) x', y, f', f x ′ , y ″ , f ′ , f ″ {\displaystyle x',y'',f',f''} {\displaystyle x',y'',f',f''} x ′ , y ″ , f ′ , f ″ {\displaystyle x',y'',f',f''\!} {\displaystyle x',y'',f',f''\!}
Derivative (HTML-yanlış) x^\prime, y^{\prime\prime} x ′ , y ′ ′ {\displaystyle x^{\prime },y^{\prime \prime }} {\displaystyle x^{\prime },y^{\prime \prime }} x ′ , y ′ ′ {\displaystyle x^{\prime },y^{\prime \prime }\,\!} {\displaystyle x^{\prime },y^{\prime \prime }\,\!}
Derivative (PNG-yanlış) x\prime, y\prime\prime x ′ , y ′ ′ {\displaystyle x\prime ,y\prime \prime } {\displaystyle x\prime ,y\prime \prime } x ′ , y ′ ′ {\displaystyle x\prime ,y\prime \prime \,\!} {\displaystyle x\prime ,y\prime \prime \,\!}
Derivative dots \dot{x}, \ddot{x} x ˙ , x ¨ {\displaystyle {\dot {x}},{\ddot {x}}} {\displaystyle {\dot {x}},{\ddot {x}}}
Underlines, overlines, vectors \hat a \ \bar b \ \vec c a ^   b ¯   c → {\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}} {\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}}
\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} a b →   c d ←   d e f ^ {\displaystyle {\overrightarrow {ab}}\ {\overleftarrow {cd}}\ {\widehat {def}}} {\displaystyle {\overrightarrow {ab}}\ {\overleftarrow {cd}}\ {\widehat {def}}}
\overline{g h i} \ \underline{j k l} g h i ¯   j k l _ {\displaystyle {\overline {ghi}}\ {\underline {jkl}}} {\displaystyle {\overline {ghi}}\ {\underline {jkl}}}
Arrows A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C A ← n + μ − 1 B → T n ± i − 1 C {\displaystyle A{\xleftarrow {n+\mu -1}}B{\xrightarrow[{T}]{n\pm i-1}}C} {\displaystyle A\xleftarrow {n+\mu -1} B{\xrightarrow[{T}]{n\pm i-1}}C}
Overbraces \overbrace{ 1+2+\cdots+100 }^{5050} 1 + 2 + ⋯ + 100 ⏞ 5050 {\displaystyle \overbrace {1+2+\cdots +100} ^{5050}} {\displaystyle \overbrace {1+2+\cdots +100} ^{5050}}
Underbraces \underbrace{ a+b+\cdots+z }_{26} a + b + ⋯ + z ⏟ 26 {\displaystyle \underbrace {a+b+\cdots +z} _{26}} {\displaystyle \underbrace {a+b+\cdots +z} _{26}}
Sum \sum_{k=1}^N k^2 ∑ k = 1 N k 2 {\displaystyle \sum _{k=1}^{N}k^{2}} {\displaystyle \sum _{k=1}^{N}k^{2}}
Sum (force \textstyle) \textstyle \sum_{k=1}^N k^2 ∑ k = 1 N k 2 {\displaystyle \textstyle \sum _{k=1}^{N}k^{2}} {\displaystyle \textstyle \sum _{k=1}^{N}k^{2}}
Product \prod_{i=1}^N x_i ∏ i = 1 N x i {\displaystyle \prod _{i=1}^{N}x_{i}} {\displaystyle \prod _{i=1}^{N}x_{i}}
Product (force \textstyle) \textstyle \prod_{i=1}^N x_i ∏ i = 1 N x i {\displaystyle \textstyle \prod _{i=1}^{N}x_{i}} {\displaystyle \textstyle \prod _{i=1}^{N}x_{i}}
Coproduct \coprod_{i=1}^N x_i ∐ i = 1 N x i {\displaystyle \coprod _{i=1}^{N}x_{i}} {\displaystyle \coprod _{i=1}^{N}x_{i}}
Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i ∐ i = 1 N x i {\displaystyle \textstyle \coprod _{i=1}^{N}x_{i}} {\displaystyle \textstyle \coprod _{i=1}^{N}x_{i}}
Limit \lim_{n \to \infty}x_n lim n → ∞ x n {\displaystyle \lim _{n\to \infty }x_{n}} {\displaystyle \lim _{n\to \infty }x_{n}}
Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n lim n → ∞ x n {\displaystyle \textstyle \lim _{n\to \infty }x_{n}} {\displaystyle \textstyle \lim _{n\to \infty }x_{n}}
Integral \int_{-N}^{N} e^x\, dx ∫ − N N e x d x {\displaystyle \int _{-N}^{N}e^{x}\,dx} {\displaystyle \int _{-N}^{N}e^{x}\,dx}
İntegral (force \textstyle) \textstyle \int_{-N}^{N} e^x\, dx ∫ − N N e x d x {\displaystyle \textstyle \int _{-N}^{N}e^{x}\,dx} {\displaystyle \textstyle \int _{-N}^{N}e^{x}\,dx}
Çift katlı integral \iint_{D}^{W} \, dx\,dy ∬ D W d x d y {\displaystyle \iint _{D}^{W}\,dx\,dy} {\displaystyle \iint _{D}^{W}\,dx\,dy}
Üç katlı integral \iiint_{E}^{V} \, dx\,dy\,dz ∭ E V d x d y d z {\displaystyle \iiint _{E}^{V}\,dx\,dy\,dz} {\displaystyle \iiint _{E}^{V}\,dx\,dy\,dz}
Dört katlı integral \iiiint_{F}^{U} \, dx\,dy\,dz\,dt ⨌ F U d x d y d z d t {\displaystyle \iiiint _{F}^{U}\,dx\,dy\,dz\,dt} {\displaystyle \iiiint _{F}^{U}\,dx\,dy\,dz\,dt}
Path integral \oint_{C} x^3\, dx + 4y^2\, dy ∮ C x 3 d x + 4 y 2 d y {\displaystyle \oint _{C}x^{3}\,dx+4y^{2}\,dy} {\displaystyle \oint _{C}x^{3}\,dx+4y^{2}\,dy}
Intersections \bigcap_1^{n} p ⋂ 1 n p {\displaystyle \bigcap _{1}^{n}p} {\displaystyle \bigcap _{1}^{n}p}
Unions \bigcup_1^{k} p ⋃ 1 k p {\displaystyle \bigcup _{1}^{k}p} {\displaystyle \bigcup _{1}^{k}p}

Fractions, matrices, multilines

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Feature Syntax How it looks rendered
Fractions \frac{2}{4}=0.5 2 4 = 0.5 {\displaystyle {\frac {2}{4}}=0.5} {\displaystyle {\frac {2}{4}}=0.5}
Small Fractions \tfrac{2}{4} = 0.5 2 4 = 0.5 {\displaystyle {\tfrac {2}{4}}=0.5} {\displaystyle {\tfrac {2}{4}}=0.5}
Large (normal) Fractions \dfrac{2}{4} = 0.5 2 4 = 0.5 {\displaystyle {\dfrac {2}{4}}=0.5} {\displaystyle {\dfrac {2}{4}}=0.5}
Large (nestled) Fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a 2 c + 2 d + 2 4 = a {\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a} {\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a}
Binomial coefficients \binom{n}{k} ( n k ) {\displaystyle {\binom {n}{k}}} {\displaystyle {\binom {n}{k}}}
Small Binomial coefficients \tbinom{n}{k} ( n k ) {\displaystyle {\tbinom {n}{k}}} {\displaystyle {\tbinom {n}{k}}}
Large (normal) Binomial coefficients \dbinom{n}{k} ( n k ) {\displaystyle {\dbinom {n}{k}}} {\displaystyle {\dbinom {n}{k}}}
Matrices 
\begin{matrix}
  x & y \\
  z & v 
\end{matrix}
 x y z v {\displaystyle {\begin{matrix}x&y\\z&v\end{matrix}}} {\displaystyle {\begin{matrix}x&y\\z&v\end{matrix}}} 
\begin{vmatrix}
  x & y \\
  z & v 
\end{vmatrix}
 | x y z v | {\displaystyle {\begin{vmatrix}x&y\\z&v\end{vmatrix}}} {\displaystyle {\begin{vmatrix}x&y\\z&v\end{vmatrix}}} 
\begin{Vmatrix}
  x & y \\
  z & v
\end{Vmatrix}
 ‖ x y z v ‖ {\displaystyle {\begin{Vmatrix}x&y\\z&v\end{Vmatrix}}} {\displaystyle {\begin{Vmatrix}x&y\\z&v\end{Vmatrix}}} 
\begin{bmatrix}
  0      & \cdots & 0      \\
  \vdots & \ddots & \vdots \\ 
  0      & \cdots & 0
\end{bmatrix}
 [ 0 ⋯ 0 ⋮ ⋱ ⋮ 0 ⋯ 0 ] {\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}} {\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}} 
\begin{Bmatrix}
  x & y \\
  z & v
\end{Bmatrix}
 { x y z v } {\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}} {\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}} 
\begin{pmatrix}
  x & y \\
  z & v 
\end{pmatrix}
 ( x y z v ) {\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}} {\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}} 
\bigl( \begin{smallmatrix}
  a&b\\ c&d
\end{smallmatrix} \bigr)
( a b c d ) {\displaystyle {\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}} {\displaystyle {\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}}
Case distinctions 
f(n) = 
\begin{cases} 
  n/2,  & \mbox{if }n\mbox{ is even} \\
  3n+1, & \mbox{if }n\mbox{ is odd} 
\end{cases}
 f ( n ) = { n / 2 , if  n  is even 3 n + 1 , if  n  is odd {\displaystyle f(n)={\begin{cases}n/2,&{\mbox{if }}n{\mbox{ is even}}\\3n+1,&{\mbox{if }}n{\mbox{ is odd}}\end{cases}}} {\displaystyle f(n)={\begin{cases}n/2,&{\mbox{if }}n{\mbox{ is even}}\\3n+1,&{\mbox{if }}n{\mbox{ is odd}}\end{cases}}}
Multiline equations 
\begin{align}
 f(x) & = (a+b)^2 \\
      & = a^2+2ab+b^2 \\
\end{align}
f ( x ) = ( a + b ) 2 = a 2 + 2 a b + b 2 {\displaystyle {\begin{aligned}f(x)&=(a+b)^{2}\\&=a^{2}+2ab+b^{2}\\\end{aligned}}} {\displaystyle {\begin{aligned}f(x)&=(a+b)^{2}\\&=a^{2}+2ab+b^{2}\\\end{aligned}}} 
\begin{alignat}{2}
 f(x) & = (a-b)^2 \\
      & = a^2-2ab+b^2 \\
\end{alignat}
f ( x ) = ( a − b ) 2 = a 2 − 2 a b + b 2 {\displaystyle {\begin{alignedat}{2}f(x)&=(a-b)^{2}\\&=a^{2}-2ab+b^{2}\\\end{alignedat}}} {\displaystyle {\begin{alignedat}{2}f(x)&=(a-b)^{2}\\&=a^{2}-2ab+b^{2}\\\end{alignedat}}}
Multiline equations (must define number of colums used ({lcr}) (should not be used unless needed) 
\begin{array}{lcl}
  z        & = & a \\
  f(x,y,z) & = & x + y + z  
\end{array}
 z = a f ( x , y , z ) = x + y + z {\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}} {\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}
Multiline equations (more) 
\begin{array}{lcr}
  z        & = & a \\
  f(x,y,z) & = & x + y + z     
\end{array}
 z = a f ( x , y , z ) = x + y + z {\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}} {\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}
Breaking up a long expression so that it wraps when necessary 

<math>f(x) \,\!</math>
<math>= \sum_{n=0}^\infty a_n x^n </math>
<math>= a_0+a_1x+a_2x^2+\cdots</math>

f ( x ) {\displaystyle f(x)\,\!} {\displaystyle f(x)\,\!} = ∑ n = 0 ∞ a n x n {\displaystyle =\sum _{n=0}^{\infty }a_{n}x^{n}} {\displaystyle =\sum _{n=0}^{\infty }a_{n}x^{n}} = a 0 + a 1 x + a 2 x 2 + ⋯ {\displaystyle =a_{0}+a_{1}x+a_{2}x^{2}+\cdots } {\displaystyle =a_{0}+a_{1}x+a_{2}x^{2}+\cdots }

Simultaneous equations 
\begin{cases}
    3x + 5y +  z \\
    7x - 2y + 4z \\
   -6x + 3y + 2z 
\end{cases}
 { 3 x + 5 y + z 7 x − 2 y + 4 z − 6 x + 3 y + 2 z {\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}} {\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}}

Alphabets and typefaces

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Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta A B Γ Δ E Z {\displaystyle \mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \,\!} {\displaystyle \mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \,\!}
\Eta \Theta \Iota \Kappa \Lambda \Mu H Θ I K Λ M {\displaystyle \mathrm {H} \Theta \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \,\!} {\displaystyle \mathrm {H} \Theta \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \,\!}
\Nu \Xi \Pi \Rho \Sigma \Tau N Ξ Π P Σ T {\displaystyle \mathrm {N} \Xi \Pi \mathrm {P} \Sigma \mathrm {T} \,\!} {\displaystyle \mathrm {N} \Xi \Pi \mathrm {P} \Sigma \mathrm {T} \,\!}
\Upsilon \Phi \Chi \Psi \Omega Υ Φ X Ψ Ω {\displaystyle \Upsilon \Phi \mathrm {X} \Psi \Omega \,\!} {\displaystyle \Upsilon \Phi \mathrm {X} \Psi \Omega \,\!}
\alpha \beta \gamma \delta \epsilon \zeta α β γ δ ϵ ζ {\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \,\!} {\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \,\!}
\eta \theta \iota \kappa \lambda \mu η θ ι κ λ μ {\displaystyle \eta \theta \iota \kappa \lambda \mu \,\!} {\displaystyle \eta \theta \iota \kappa \lambda \mu \,\!}
\nu \xi \pi \rho \sigma \tau ν ξ π ρ σ τ {\displaystyle \nu \xi \pi \rho \sigma \tau \,\!} {\displaystyle \nu \xi \pi \rho \sigma \tau \,\!}
\upsilon \phi \chi \psi \omega υ ϕ χ ψ ω {\displaystyle \upsilon \phi \chi \psi \omega \,\!} {\displaystyle \upsilon \phi \chi \psi \omega \,\!}
\varepsilon \digamma \vartheta \varkappa ε ϝ ϑ ϰ {\displaystyle \varepsilon \digamma \vartheta \varkappa \,\!} {\displaystyle \varepsilon \digamma \vartheta \varkappa \,\!}
\varpi \varrho \varsigma \varphi ϖ ϱ ς φ {\displaystyle \varpi \varrho \varsigma \varphi \,\!} {\displaystyle \varpi \varrho \varsigma \varphi \,\!}
Blackboard Bold/Scripts
\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} A B C D E F G {\displaystyle \mathbb {A} \mathbb {B} \mathbb {C} \mathbb {D} \mathbb {E} \mathbb {F} \mathbb {G} \,\!} {\displaystyle \mathbb {A} \mathbb {B} \mathbb {C} \mathbb {D} \mathbb {E} \mathbb {F} \mathbb {G} \,\!}
\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} H I J K L M {\displaystyle \mathbb {H} \mathbb {I} \mathbb {J} \mathbb {K} \mathbb {L} \mathbb {M} \,\!} {\displaystyle \mathbb {H} \mathbb {I} \mathbb {J} \mathbb {K} \mathbb {L} \mathbb {M} \,\!}
\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} N O P Q R S T {\displaystyle \mathbb {N} \mathbb {O} \mathbb {P} \mathbb {Q} \mathbb {R} \mathbb {S} \mathbb {T} \,\!} {\displaystyle \mathbb {N} \mathbb {O} \mathbb {P} \mathbb {Q} \mathbb {R} \mathbb {S} \mathbb {T} \,\!}
\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z} U V W X Y Z {\displaystyle \mathbb {U} \mathbb {V} \mathbb {W} \mathbb {X} \mathbb {Y} \mathbb {Z} \,\!} {\displaystyle \mathbb {U} \mathbb {V} \mathbb {W} \mathbb {X} \mathbb {Y} \mathbb {Z} \,\!}
boldface (vectors)
\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} A B C D E F G {\displaystyle \mathbf {A} \mathbf {B} \mathbf {C} \mathbf {D} \mathbf {E} \mathbf {F} \mathbf {G} \,\!} {\displaystyle \mathbf {A} \mathbf {B} \mathbf {C} \mathbf {D} \mathbf {E} \mathbf {F} \mathbf {G} \,\!}
\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} H I J K L M {\displaystyle \mathbf {H} \mathbf {I} \mathbf {J} \mathbf {K} \mathbf {L} \mathbf {M} \,\!} {\displaystyle \mathbf {H} \mathbf {I} \mathbf {J} \mathbf {K} \mathbf {L} \mathbf {M} \,\!}
\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} N O P Q R S T {\displaystyle \mathbf {N} \mathbf {O} \mathbf {P} \mathbf {Q} \mathbf {R} \mathbf {S} \mathbf {T} \,\!} {\displaystyle \mathbf {N} \mathbf {O} \mathbf {P} \mathbf {Q} \mathbf {R} \mathbf {S} \mathbf {T} \,\!}
\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} U V W X Y Z {\displaystyle \mathbf {U} \mathbf {V} \mathbf {W} \mathbf {X} \mathbf {Y} \mathbf {Z} \,\!} {\displaystyle \mathbf {U} \mathbf {V} \mathbf {W} \mathbf {X} \mathbf {Y} \mathbf {Z} \,\!}
\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} a b c d e f g {\displaystyle \mathbf {a} \mathbf {b} \mathbf {c} \mathbf {d} \mathbf {e} \mathbf {f} \mathbf {g} \,\!} {\displaystyle \mathbf {a} \mathbf {b} \mathbf {c} \mathbf {d} \mathbf {e} \mathbf {f} \mathbf {g} \,\!}
\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} h i j k l m {\displaystyle \mathbf {h} \mathbf {i} \mathbf {j} \mathbf {k} \mathbf {l} \mathbf {m} \,\!} {\displaystyle \mathbf {h} \mathbf {i} \mathbf {j} \mathbf {k} \mathbf {l} \mathbf {m} \,\!}
\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} n o p q r s t {\displaystyle \mathbf {n} \mathbf {o} \mathbf {p} \mathbf {q} \mathbf {r} \mathbf {s} \mathbf {t} \,\!} {\displaystyle \mathbf {n} \mathbf {o} \mathbf {p} \mathbf {q} \mathbf {r} \mathbf {s} \mathbf {t} \,\!}
\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} u v w x y z {\displaystyle \mathbf {u} \mathbf {v} \mathbf {w} \mathbf {x} \mathbf {y} \mathbf {z} \,\!} {\displaystyle \mathbf {u} \mathbf {v} \mathbf {w} \mathbf {x} \mathbf {y} \mathbf {z} \,\!}
\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} 0 1 2 3 4 {\displaystyle \mathbf {0} \mathbf {1} \mathbf {2} \mathbf {3} \mathbf {4} \,\!} {\displaystyle \mathbf {0} \mathbf {1} \mathbf {2} \mathbf {3} \mathbf {4} \,\!}
\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9} 5 6 7 8 9 {\displaystyle \mathbf {5} \mathbf {6} \mathbf {7} \mathbf {8} \mathbf {9} \,\!} {\displaystyle \mathbf {5} \mathbf {6} \mathbf {7} \mathbf {8} \mathbf {9} \,\!}
Boldface (greek)
\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} A B Γ Δ E Z {\displaystyle {\boldsymbol {\mathrm {A} }}{\boldsymbol {\mathrm {B} }}{\boldsymbol {\Gamma }}{\boldsymbol {\Delta }}{\boldsymbol {\mathrm {E} }}{\boldsymbol {\mathrm {Z} }}\,\!} {\displaystyle {\boldsymbol {\mathrm {A} }}{\boldsymbol {\mathrm {B} }}{\boldsymbol {\Gamma }}{\boldsymbol {\Delta }}{\boldsymbol {\mathrm {E} }}{\boldsymbol {\mathrm {Z} }}\,\!}
\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu} H Θ I K Λ M {\displaystyle {\boldsymbol {\mathrm {H} }}{\boldsymbol {\Theta }}{\boldsymbol {\mathrm {I} }}{\boldsymbol {\mathrm {K} }}{\boldsymbol {\Lambda }}{\boldsymbol {\mathrm {M} }}\,\!} {\displaystyle {\boldsymbol {\mathrm {H} }}{\boldsymbol {\Theta }}{\boldsymbol {\mathrm {I} }}{\boldsymbol {\mathrm {K} }}{\boldsymbol {\Lambda }}{\boldsymbol {\mathrm {M} }}\,\!}
\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau} N Ξ Π P Σ T {\displaystyle {\boldsymbol {\mathrm {N} }}{\boldsymbol {\Xi }}{\boldsymbol {\Pi }}{\boldsymbol {\mathrm {P} }}{\boldsymbol {\Sigma }}{\boldsymbol {\mathrm {T} }}\,\!} {\displaystyle {\boldsymbol {\mathrm {N} }}{\boldsymbol {\Xi }}{\boldsymbol {\Pi }}{\boldsymbol {\mathrm {P} }}{\boldsymbol {\Sigma }}{\boldsymbol {\mathrm {T} }}\,\!}
\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega} Υ Φ X Ψ Ω {\displaystyle {\boldsymbol {\Upsilon }}{\boldsymbol {\Phi }}{\boldsymbol {\mathrm {X} }}{\boldsymbol {\Psi }}{\boldsymbol {\Omega }}\,\!} {\displaystyle {\boldsymbol {\Upsilon }}{\boldsymbol {\Phi }}{\boldsymbol {\mathrm {X} }}{\boldsymbol {\Psi }}{\boldsymbol {\Omega }}\,\!}
\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta} α β γ δ ϵ ζ {\displaystyle {\boldsymbol {\alpha }}{\boldsymbol {\beta }}{\boldsymbol {\gamma }}{\boldsymbol {\delta }}{\boldsymbol {\epsilon }}{\boldsymbol {\zeta }}\,\!} {\displaystyle {\boldsymbol {\alpha }}{\boldsymbol {\beta }}{\boldsymbol {\gamma }}{\boldsymbol {\delta }}{\boldsymbol {\epsilon }}{\boldsymbol {\zeta }}\,\!}
\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu} η θ ι κ λ μ {\displaystyle {\boldsymbol {\eta }}{\boldsymbol {\theta }}{\boldsymbol {\iota }}{\boldsymbol {\kappa }}{\boldsymbol {\lambda }}{\boldsymbol {\mu }}\,\!} {\displaystyle {\boldsymbol {\eta }}{\boldsymbol {\theta }}{\boldsymbol {\iota }}{\boldsymbol {\kappa }}{\boldsymbol {\lambda }}{\boldsymbol {\mu }}\,\!}
\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau} ν ξ π ρ σ τ {\displaystyle {\boldsymbol {\nu }}{\boldsymbol {\xi }}{\boldsymbol {\pi }}{\boldsymbol {\rho }}{\boldsymbol {\sigma }}{\boldsymbol {\tau }}\,\!} {\displaystyle {\boldsymbol {\nu }}{\boldsymbol {\xi }}{\boldsymbol {\pi }}{\boldsymbol {\rho }}{\boldsymbol {\sigma }}{\boldsymbol {\tau }}\,\!}
\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega} υ ϕ χ ψ ω {\displaystyle {\boldsymbol {\upsilon }}{\boldsymbol {\phi }}{\boldsymbol {\chi }}{\boldsymbol {\psi }}{\boldsymbol {\omega }}\,\!} {\displaystyle {\boldsymbol {\upsilon }}{\boldsymbol {\phi }}{\boldsymbol {\chi }}{\boldsymbol {\psi }}{\boldsymbol {\omega }}\,\!}
\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} ε ϝ ϑ ϰ {\displaystyle {\boldsymbol {\varepsilon }}{\boldsymbol {\digamma }}{\boldsymbol {\vartheta }}{\boldsymbol {\varkappa }}\,\!} {\displaystyle {\boldsymbol {\varepsilon }}{\boldsymbol {\digamma }}{\boldsymbol {\vartheta }}{\boldsymbol {\varkappa }}\,\!}
\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi} ϖ ϱ ς φ {\displaystyle {\boldsymbol {\varpi }}{\boldsymbol {\varrho }}{\boldsymbol {\varsigma }}{\boldsymbol {\varphi }}\,\!} {\displaystyle {\boldsymbol {\varpi }}{\boldsymbol {\varrho }}{\boldsymbol {\varsigma }}{\boldsymbol {\varphi }}\,\!}
Italics
\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} A B C D E F G {\displaystyle {\mathit {A}}{\mathit {B}}{\mathit {C}}{\mathit {D}}{\mathit {E}}{\mathit {F}}{\mathit {G}}\,\!} {\displaystyle {\mathit {A}}{\mathit {B}}{\mathit {C}}{\mathit {D}}{\mathit {E}}{\mathit {F}}{\mathit {G}}\,\!}
\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} H I J K L M {\displaystyle {\mathit {H}}{\mathit {I}}{\mathit {J}}{\mathit {K}}{\mathit {L}}{\mathit {M}}\,\!} {\displaystyle {\mathit {H}}{\mathit {I}}{\mathit {J}}{\mathit {K}}{\mathit {L}}{\mathit {M}}\,\!}
\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} N O P Q R S T {\displaystyle {\mathit {N}}{\mathit {O}}{\mathit {P}}{\mathit {Q}}{\mathit {R}}{\mathit {S}}{\mathit {T}}\,\!} {\displaystyle {\mathit {N}}{\mathit {O}}{\mathit {P}}{\mathit {Q}}{\mathit {R}}{\mathit {S}}{\mathit {T}}\,\!}
\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} U V W X Y Z {\displaystyle {\mathit {U}}{\mathit {V}}{\mathit {W}}{\mathit {X}}{\mathit {Y}}{\mathit {Z}}\,\!} {\displaystyle {\mathit {U}}{\mathit {V}}{\mathit {W}}{\mathit {X}}{\mathit {Y}}{\mathit {Z}}\,\!}
\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} a b c d e f g {\displaystyle {\mathit {a}}{\mathit {b}}{\mathit {c}}{\mathit {d}}{\mathit {e}}{\mathit {f}}{\mathit {g}}\,\!} {\displaystyle {\mathit {a}}{\mathit {b}}{\mathit {c}}{\mathit {d}}{\mathit {e}}{\mathit {f}}{\mathit {g}}\,\!}
\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} h i j k l m {\displaystyle {\mathit {h}}{\mathit {i}}{\mathit {j}}{\mathit {k}}{\mathit {l}}{\mathit {m}}\,\!} {\displaystyle {\mathit {h}}{\mathit {i}}{\mathit {j}}{\mathit {k}}{\mathit {l}}{\mathit {m}}\,\!}
\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} n o p q r s t {\displaystyle {\mathit {n}}{\mathit {o}}{\mathit {p}}{\mathit {q}}{\mathit {r}}{\mathit {s}}{\mathit {t}}\,\!} {\displaystyle {\mathit {n}}{\mathit {o}}{\mathit {p}}{\mathit {q}}{\mathit {r}}{\mathit {s}}{\mathit {t}}\,\!}
\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} u v w x y z {\displaystyle {\mathit {u}}{\mathit {v}}{\mathit {w}}{\mathit {x}}{\mathit {y}}{\mathit {z}}\,\!} {\displaystyle {\mathit {u}}{\mathit {v}}{\mathit {w}}{\mathit {x}}{\mathit {y}}{\mathit {z}}\,\!}
\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} 0 1 2 3 4 {\displaystyle {\mathit {0}}{\mathit {1}}{\mathit {2}}{\mathit {3}}{\mathit {4}}\,\!} {\displaystyle {\mathit {0}}{\mathit {1}}{\mathit {2}}{\mathit {3}}{\mathit {4}}\,\!}
\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9} 5 6 7 8 9 {\displaystyle {\mathit {5}}{\mathit {6}}{\mathit {7}}{\mathit {8}}{\mathit {9}}\,\!} {\displaystyle {\mathit {5}}{\mathit {6}}{\mathit {7}}{\mathit {8}}{\mathit {9}}\,\!}
Roman typeface
\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} A B C D E F G {\displaystyle \mathrm {A} \mathrm {B} \mathrm {C} \mathrm {D} \mathrm {E} \mathrm {F} \mathrm {G} \,\!} {\displaystyle \mathrm {A} \mathrm {B} \mathrm {C} \mathrm {D} \mathrm {E} \mathrm {F} \mathrm {G} \,\!}
\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} H I J K L M {\displaystyle \mathrm {H} \mathrm {I} \mathrm {J} \mathrm {K} \mathrm {L} \mathrm {M} \,\!} {\displaystyle \mathrm {H} \mathrm {I} \mathrm {J} \mathrm {K} \mathrm {L} \mathrm {M} \,\!}
\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} N O P Q R S T {\displaystyle \mathrm {N} \mathrm {O} \mathrm {P} \mathrm {Q} \mathrm {R} \mathrm {S} \mathrm {T} \,\!} {\displaystyle \mathrm {N} \mathrm {O} \mathrm {P} \mathrm {Q} \mathrm {R} \mathrm {S} \mathrm {T} \,\!}
\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} U V W X Y Z {\displaystyle \mathrm {U} \mathrm {V} \mathrm {W} \mathrm {X} \mathrm {Y} \mathrm {Z} \,\!} {\displaystyle \mathrm {U} \mathrm {V} \mathrm {W} \mathrm {X} \mathrm {Y} \mathrm {Z} \,\!}
\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g} a b c d e f g {\displaystyle \mathrm {a} \mathrm {b} \mathrm {c} \mathrm {d} \mathrm {e} \mathrm {f} \mathrm {g} \,\!} {\displaystyle \mathrm {a} \mathrm {b} \mathrm {c} \mathrm {d} \mathrm {e} \mathrm {f} \mathrm {g} \,\!}
\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} h i j k l m {\displaystyle \mathrm {h} \mathrm {i} \mathrm {j} \mathrm {k} \mathrm {l} \mathrm {m} \,\!} {\displaystyle \mathrm {h} \mathrm {i} \mathrm {j} \mathrm {k} \mathrm {l} \mathrm {m} \,\!}
\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} n o p q r s t {\displaystyle \mathrm {n} \mathrm {o} \mathrm {p} \mathrm {q} \mathrm {r} \mathrm {s} \mathrm {t} \,\!} {\displaystyle \mathrm {n} \mathrm {o} \mathrm {p} \mathrm {q} \mathrm {r} \mathrm {s} \mathrm {t} \,\!}
\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} u v w x y z {\displaystyle \mathrm {u} \mathrm {v} \mathrm {w} \mathrm {x} \mathrm {y} \mathrm {z} \,\!} {\displaystyle \mathrm {u} \mathrm {v} \mathrm {w} \mathrm {x} \mathrm {y} \mathrm {z} \,\!}
\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} 0 1 2 3 4 {\displaystyle \mathrm {0} \mathrm {1} \mathrm {2} \mathrm {3} \mathrm {4} \,\!} {\displaystyle \mathrm {0} \mathrm {1} \mathrm {2} \mathrm {3} \mathrm {4} \,\!}
\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9} 5 6 7 8 9 {\displaystyle \mathrm {5} \mathrm {6} \mathrm {7} \mathrm {8} \mathrm {9} \,\!} {\displaystyle \mathrm {5} \mathrm {6} \mathrm {7} \mathrm {8} \mathrm {9} \,\!}
Fraktur typeface
\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} A B C D E F G {\displaystyle {\mathfrak {A}}{\mathfrak {B}}{\mathfrak {C}}{\mathfrak {D}}{\mathfrak {E}}{\mathfrak {F}}{\mathfrak {G}}\,\!} {\displaystyle {\mathfrak {A}}{\mathfrak {B}}{\mathfrak {C}}{\mathfrak {D}}{\mathfrak {E}}{\mathfrak {F}}{\mathfrak {G}}\,\!}
\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} H I J K L M {\displaystyle {\mathfrak {H}}{\mathfrak {I}}{\mathfrak {J}}{\mathfrak {K}}{\mathfrak {L}}{\mathfrak {M}}\,\!} {\displaystyle {\mathfrak {H}}{\mathfrak {I}}{\mathfrak {J}}{\mathfrak {K}}{\mathfrak {L}}{\mathfrak {M}}\,\!}
\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} N O P Q R S T {\displaystyle {\mathfrak {N}}{\mathfrak {O}}{\mathfrak {P}}{\mathfrak {Q}}{\mathfrak {R}}{\mathfrak {S}}{\mathfrak {T}}\,\!} {\displaystyle {\mathfrak {N}}{\mathfrak {O}}{\mathfrak {P}}{\mathfrak {Q}}{\mathfrak {R}}{\mathfrak {S}}{\mathfrak {T}}\,\!}
\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} U V W X Y Z {\displaystyle {\mathfrak {U}}{\mathfrak {V}}{\mathfrak {W}}{\mathfrak {X}}{\mathfrak {Y}}{\mathfrak {Z}}\,\!} {\displaystyle {\mathfrak {U}}{\mathfrak {V}}{\mathfrak {W}}{\mathfrak {X}}{\mathfrak {Y}}{\mathfrak {Z}}\,\!}
\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} a b c d e f g {\displaystyle {\mathfrak {a}}{\mathfrak {b}}{\mathfrak {c}}{\mathfrak {d}}{\mathfrak {e}}{\mathfrak {f}}{\mathfrak {g}}\,\!} {\displaystyle {\mathfrak {a}}{\mathfrak {b}}{\mathfrak {c}}{\mathfrak {d}}{\mathfrak {e}}{\mathfrak {f}}{\mathfrak {g}}\,\!}
\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} h i j k l m {\displaystyle {\mathfrak {h}}{\mathfrak {i}}{\mathfrak {j}}{\mathfrak {k}}{\mathfrak {l}}{\mathfrak {m}}\,\!} {\displaystyle {\mathfrak {h}}{\mathfrak {i}}{\mathfrak {j}}{\mathfrak {k}}{\mathfrak {l}}{\mathfrak {m}}\,\!}
\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} n o p q r s t {\displaystyle {\mathfrak {n}}{\mathfrak {o}}{\mathfrak {p}}{\mathfrak {q}}{\mathfrak {r}}{\mathfrak {s}}{\mathfrak {t}}\,\!} {\displaystyle {\mathfrak {n}}{\mathfrak {o}}{\mathfrak {p}}{\mathfrak {q}}{\mathfrak {r}}{\mathfrak {s}}{\mathfrak {t}}\,\!}
\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} u v w x y z {\displaystyle {\mathfrak {u}}{\mathfrak {v}}{\mathfrak {w}}{\mathfrak {x}}{\mathfrak {y}}{\mathfrak {z}}\,\!} {\displaystyle {\mathfrak {u}}{\mathfrak {v}}{\mathfrak {w}}{\mathfrak {x}}{\mathfrak {y}}{\mathfrak {z}}\,\!}
\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} 0 1 2 3 4 {\displaystyle {\mathfrak {0}}{\mathfrak {1}}{\mathfrak {2}}{\mathfrak {3}}{\mathfrak {4}}\,\!} {\displaystyle {\mathfrak {0}}{\mathfrak {1}}{\mathfrak {2}}{\mathfrak {3}}{\mathfrak {4}}\,\!}
\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9} 5 6 7 8 9 {\displaystyle {\mathfrak {5}}{\mathfrak {6}}{\mathfrak {7}}{\mathfrak {8}}{\mathfrak {9}}\,\!} {\displaystyle {\mathfrak {5}}{\mathfrak {6}}{\mathfrak {7}}{\mathfrak {8}}{\mathfrak {9}}\,\!}
Calligraphy/Script
\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} A B C D E F G {\displaystyle {\mathcal {A}}{\mathcal {B}}{\mathcal {C}}{\mathcal {D}}{\mathcal {E}}{\mathcal {F}}{\mathcal {G}}\,\!} {\displaystyle {\mathcal {A}}{\mathcal {B}}{\mathcal {C}}{\mathcal {D}}{\mathcal {E}}{\mathcal {F}}{\mathcal {G}}\,\!}
\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} H I J K L M {\displaystyle {\mathcal {H}}{\mathcal {I}}{\mathcal {J}}{\mathcal {K}}{\mathcal {L}}{\mathcal {M}}\,\!} {\displaystyle {\mathcal {H}}{\mathcal {I}}{\mathcal {J}}{\mathcal {K}}{\mathcal {L}}{\mathcal {M}}\,\!}
\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} N O P Q R S T {\displaystyle {\mathcal {N}}{\mathcal {O}}{\mathcal {P}}{\mathcal {Q}}{\mathcal {R}}{\mathcal {S}}{\mathcal {T}}\,\!} {\displaystyle {\mathcal {N}}{\mathcal {O}}{\mathcal {P}}{\mathcal {Q}}{\mathcal {R}}{\mathcal {S}}{\mathcal {T}}\,\!}
\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z} U V W X Y Z {\displaystyle {\mathcal {U}}{\mathcal {V}}{\mathcal {W}}{\mathcal {X}}{\mathcal {Y}}{\mathcal {Z}}\,\!} {\displaystyle {\mathcal {U}}{\mathcal {V}}{\mathcal {W}}{\mathcal {X}}{\mathcal {Y}}{\mathcal {Z}}\,\!}
Hebrew
\aleph \beth \gimel \daleth ℵ ℶ ℷ ℸ {\displaystyle \aleph \beth \gimel \daleth \,\!} {\displaystyle \aleph \beth \gimel \daleth \,\!}
Feature Syntax How it looks rendered
non-italicised characters \mbox{abc} abc {\displaystyle {\mbox{abc}}} {\displaystyle {\mbox{abc}}} abc {\displaystyle {\mbox{abc}}\,\!} {\displaystyle {\mbox{abc}}\,\!}
mixed italics (bad) \mbox{if} n \mbox{is even} if n is even {\displaystyle {\mbox{if}}n{\mbox{is even}}} {\displaystyle {\mbox{if}}n{\mbox{is even}}} if n is even {\displaystyle {\mbox{if}}n{\mbox{is even}}\,\!} {\displaystyle {\mbox{if}}n{\mbox{is even}}\,\!}
mixed italics (good) \mbox{if }n\mbox{ is even} if  n  is even {\displaystyle {\mbox{if }}n{\mbox{ is even}}} {\displaystyle {\mbox{if }}n{\mbox{ is even}}} if  n  is even {\displaystyle {\mbox{if }}n{\mbox{ is even}}\,\!} {\displaystyle {\mbox{if }}n{\mbox{ is even}}\,\!}
mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space) \mbox{if}~n\ \mbox{is even} if   n   is even {\displaystyle {\mbox{if}}~n\ {\mbox{is even}}} {\displaystyle {\mbox{if}}~n\ {\mbox{is even}}} if   n   is even {\displaystyle {\mbox{if}}~n\ {\mbox{is even}}\,\!} {\displaystyle {\mbox{if}}~n\ {\mbox{is even}}\,\!}

Parenthesizing big expressions, brackets, bars

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Feature Syntax How it looks rendered
Bad ( \frac{1}{2} ) ( 1 2 ) {\displaystyle ({\frac {1}{2}})} {\displaystyle ({\frac {1}{2}})}
Good \left ( \frac{1}{2} \right ) ( 1 2 ) {\displaystyle \left({\frac {1}{2}}\right)} {\displaystyle \left({\frac {1}{2}}\right)}

You can use various delimiters with \left and \right:

Feature Syntax How it looks rendered
Parentheses \left ( \frac{a}{b} \right ) ( a b ) {\displaystyle \left({\frac {a}{b}}\right)} {\displaystyle \left({\frac {a}{b}}\right)}
Brackets \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack [ a b ] [ a b ] {\displaystyle \left[{\frac {a}{b}}\right]\quad \left\lbrack {\frac {a}{b}}\right\rbrack } {\displaystyle \left[{\frac {a}{b}}\right]\quad \left\lbrack {\frac {a}{b}}\right\rbrack }
Braces \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace { a b } { a b } {\displaystyle \left\{{\frac {a}{b}}\right\}\quad \left\lbrace {\frac {a}{b}}\right\rbrace } {\displaystyle \left\{{\frac {a}{b}}\right\}\quad \left\lbrace {\frac {a}{b}}\right\rbrace }
Angle brackets \left \langle \frac{a}{b} \right \rangle ⟨ a b ⟩ {\displaystyle \left\langle {\frac {a}{b}}\right\rangle } {\displaystyle \left\langle {\frac {a}{b}}\right\rangle }
Bars and double bars \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \| | a b | ‖ c d ‖ {\displaystyle \left|{\frac {a}{b}}\right\vert \left\Vert {\frac {c}{d}}\right\|} {\displaystyle \left|{\frac {a}{b}}\right\vert \left\Vert {\frac {c}{d}}\right\|}
Floor and ceiling functions: \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil ⌊ a b ⌋ ⌈ c d ⌉ {\displaystyle \left\lfloor {\frac {a}{b}}\right\rfloor \left\lceil {\frac {c}{d}}\right\rceil } {\displaystyle \left\lfloor {\frac {a}{b}}\right\rfloor \left\lceil {\frac {c}{d}}\right\rceil }
Slashes and backslashes \left / \frac{a}{b} \right \backslash / a b \ {\displaystyle \left/{\frac {a}{b}}\right\backslash } {\displaystyle \left/{\frac {a}{b}}\right\backslash }
Up, down and up-down arrows \left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow ↑ a b ↓ ⇑ a b ⇓ ↕ a b ⇕ {\displaystyle \left\uparrow {\frac {a}{b}}\right\downarrow \quad \left\Uparrow {\frac {a}{b}}\right\Downarrow \quad \left\updownarrow {\frac {a}{b}}\right\Updownarrow } {\displaystyle \left\uparrow {\frac {a}{b}}\right\downarrow \quad \left\Uparrow {\frac {a}{b}}\right\Downarrow \quad \left\updownarrow {\frac {a}{b}}\right\Updownarrow }

Delimiters can be mixed,
as long as \left and \right match

\left [ 0,1 \right )
\left \langle \psi \right |

[ 0 , 1 ) {\displaystyle \left[0,1\right)} {\displaystyle \left[0,1\right)}
⟨ ψ | {\displaystyle \left\langle \psi \right|} {\displaystyle \left\langle \psi \right|}

Use \left. and \right. if you don't
want a delimiter to appear:		 \left . \frac{A}{B} \right \} \to X A B } → X {\displaystyle \left.{\frac {A}{B}}\right\}\to X} {\displaystyle \left.{\frac {A}{B}}\right\}\to X}
Size of the delimiters \big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]

( ( ( ( . . . ] ] ] ] {\displaystyle {\big (}{\Big (}{\bigg (}{\Bigg (}...{\Bigg ]}{\bigg ]}{\Big ]}{\big ]}} {\displaystyle {\big (}{\Big (}{\bigg (}{\Bigg (}...{\Bigg ]}{\bigg ]}{\Big ]}{\big ]}}

\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle

{ { { { . . . ⟩ ⟩ ⟩ ⟩ {\displaystyle {\big \{}{\Big \{}{\bigg \{}{\Bigg \{}...{\Bigg \rangle }{\bigg \rangle }{\Big \rangle }{\big \rangle }} {\displaystyle {\big \{}{\Big \{}{\bigg \{}{\Bigg \{}...{\Bigg \rangle }{\bigg \rangle }{\Big \rangle }{\big \rangle }}

\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big| ‖ ‖ ‖ ‖ . . . | | | | {\displaystyle {\big \|}{\Big \|}{\bigg \|}{\Bigg \|}...{\Bigg |}{\bigg |}{\Big |}{\big |}} {\displaystyle {\big \|}{\Big \|}{\bigg \|}{\Bigg \|}...{\Bigg |}{\bigg |}{\Big |}{\big |}}
\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil

⌊ ⌊ ⌊ ⌊ . . . ⌉ ⌉ ⌉ ⌉ {\displaystyle {\big \lfloor }{\Big \lfloor }{\bigg \lfloor }{\Bigg \lfloor }...{\Bigg \rceil }{\bigg \rceil }{\Big \rceil }{\big \rceil }} {\displaystyle {\big \lfloor }{\Big \lfloor }{\bigg \lfloor }{\Bigg \lfloor }...{\Bigg \rceil }{\bigg \rceil }{\Big \rceil }{\big \rceil }}

\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow

↑ ↑ ↑ ↑ . . . ⇓ ⇓ ⇓ ⇓ {\displaystyle {\big \uparrow }{\Big \uparrow }{\bigg \uparrow }{\Bigg \uparrow }...{\Bigg \Downarrow }{\bigg \Downarrow }{\Big \Downarrow }{\big \Downarrow }} {\displaystyle {\big \uparrow }{\Big \uparrow }{\bigg \uparrow }{\Bigg \uparrow }...{\Bigg \Downarrow }{\bigg \Downarrow }{\Big \Downarrow }{\big \Downarrow }}

\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow

↕ ↕ ↕ ↕ . . . ⇕ ⇕ ⇕ ⇕ {\displaystyle {\big \updownarrow }{\Big \updownarrow }{\bigg \updownarrow }{\Bigg \updownarrow }...{\Bigg \Updownarrow }{\bigg \Updownarrow }{\Big \Updownarrow }{\big \Updownarrow }} {\displaystyle {\big \updownarrow }{\Big \updownarrow }{\bigg \updownarrow }{\Bigg \updownarrow }...{\Bigg \Updownarrow }{\bigg \Updownarrow }{\Big \Updownarrow }{\big \Updownarrow }}

\big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash

/ / / / . . . \ \ \ \ {\displaystyle {\big /}{\Big /}{\bigg /}{\Bigg /}...{\Bigg \backslash }{\bigg \backslash }{\Big \backslash }{\big \backslash }} {\displaystyle {\big /}{\Big /}{\bigg /}{\Bigg /}...{\Bigg \backslash }{\bigg \backslash }{\Big \backslash }{\big \backslash }}

Spacing

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Note that TeX handles most spacing automatically, but you may sometimes want manual control.

Feature Syntax How it looks rendered
double quad space a \qquad b a b {\displaystyle a\qquad b} {\displaystyle a\qquad b}
quad space a \quad b a b {\displaystyle a\quad b} {\displaystyle a\quad b}
text space a\ b a   b {\displaystyle a\ b} {\displaystyle a\ b}
text space without PNG conversion a \mbox{ } b a   b {\displaystyle a{\mbox{ }}b} {\displaystyle a{\mbox{ }}b}
large space a\;b a b {\displaystyle a\;b} {\displaystyle a\;b}
medium space a\>b [not supported]
small space a\,b a b {\displaystyle a\,b} {\displaystyle a\,b}
no space ab a b {\displaystyle ab\,} {\displaystyle ab\,}
small negative space a\!b a b {\displaystyle a\!b} {\displaystyle a\!b}

Align with normal text flow

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Due to the default css 

img.tex { vertical-align: middle; }

an inline expression like ∫ − N N e x d x = 2 sinh ⁡ N {\displaystyle \int _{-N}^{N}e^{x}\,dx=2\sinh N} {\displaystyle \int _{-N}^{N}e^{x}\,dx=2\sinh N} should look good.

If you need to align it otherwise, use <font style="vertical-align:-100%;"><math>...</math></font> and play with the vertical-align argument until you get it right; however, how it looks may depend on the browser and the browser settings.

Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

Forced PNG rendering

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To force the formula to render as PNG, add \, (small space) at the end of the formula (where it is not rendered). This will force PNG if the user is in "HTML if simple" mode, but not for "HTML if possible" mode (math rendering settings in preferences).

You can also use \,\! (small space and negative space, which cancel out) anywhere inside the math tags. This does force PNG even in "HTML if possible" mode, unlike \,.

This could be useful to keep the rendering of formulae in a proof consistent, for example, or to fix formulae that render incorrectly in HTML (at one time, a^{2+2} rendered with an extra underscore), or to demonstrate how something is rendered when it would normally show up as HTML (as in the examples above).

For instance:

Syntax How it looks rendered
a^{c+2} a c + 2 {\displaystyle a^{c+2}} {\displaystyle a^{c+2}}
a^{c+2} \, a c + 2 {\displaystyle a^{c+2}\,} {\displaystyle a^{c+2}\,}
a^{\,\!c+2} a c + 2 {\displaystyle a^{\,\!c+2}} {\displaystyle a^{\,\!c+2}}
a^{b^{c+2}} a b c + 2 {\displaystyle a^{b^{c+2}}} {\displaystyle a^{b^{c+2}}} (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}} \, a b c + 2 {\displaystyle a^{b^{c+2}}\,} {\displaystyle a^{b^{c+2}}\,} (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}}\approx 5 a b c + 2 ≈ 5 {\displaystyle a^{b^{c+2}}\approx 5} {\displaystyle a^{b^{c+2}}\approx 5} (due to " ≈ {\displaystyle \approx } {\displaystyle \approx }" correctly displayed, no code "\,\!" needed)
a^{b^{\,\!c+2}} a b c + 2 {\displaystyle a^{b^{\,\!c+2}}} {\displaystyle a^{b^{\,\!c+2}}}
\int_{-N}^{N} e^x\, dx ∫ − N N e x d x {\displaystyle \int _{-N}^{N}e^{x}\,dx} {\displaystyle \int _{-N}^{N}e^{x}\,dx}


This has been tested with most of the formulae on this page, and seems to work perfectly.

You might want to include a comment in the HTML so people don't "correct" the formula by removing it:

<!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.-->

Color

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Equations can use color:

  • {\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}
    x 2 + 2 x − 1 {\displaystyle {\color {Blue}x^{2}}+{\color {Brown}2x}-{\color {OliveGreen}1}} {\displaystyle {\color {Blue}x^{2}}+{\color {Brown}2x}-{\color {OliveGreen}1}}
  • x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}
    x 1 , 2 = − b ± b 2 − 4 a c 2 a {\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {\color {Red}b^{2}-4ac}}}{2a}}} {\displaystyle x_{1,2}={\frac {-b\pm {\sqrt {\color {Red}b^{2}-4ac}}}{2a}}}

See here for all named colours supported by LaTeX.

Note that color should not be used as the only way to identify something because color blind people may not be able to distinguish between the two colors. See .

Examples

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Quadratic Polynomial

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        a
        
          x
          
            2
          
        
        +
        b
        x
        +
        c
        =
        0
      
    
    {\displaystyle ax^{2}+bx+c=0}
  
{\displaystyle ax^{2}+bx+c=0}

<math>ax^2 + bx + c = 0</math>

Quadratic Polynomial (Force PNG Rendering)

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        a
        
          x
          
            2
          
        
        +
        b
        x
        +
        c
        =
        0
        
        
      
    
    {\displaystyle ax^{2}+bx+c=0\,\!}
  
{\displaystyle ax^{2}+bx+c=0\,\!}

<math>ax^2 + bx + c = 0\,\!</math>

Quadratic Formula

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        x
        =
        
          
            
              −
              b
              ±
              
                
                  
                    b
                    
                      2
                    
                  
                  −
                  4
                  a
                  c
                
              
            
            
              2
              a
            
          
        
      
    
    {\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}
  
{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}

<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

Tall Parentheses and Fractions

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        2
        =
        
          (
          
            
              
                
                  (
                  
                    3
                    −
                    x
                  
                  )
                
                ×
                2
              
              
                3
                −
                x
              
            
          
          )
        
      
    
    {\displaystyle 2=\left({\frac {\left(3-x\right)\times 2}{3-x}}\right)}
  
{\displaystyle 2=\left({\frac {\left(3-x\right)\times 2}{3-x}}\right)}

<math>2 = \left(
 \frac{\left(3-x\right) \times 2}{3-x}
 \right)</math>


  
    
      
        
          S
          
            n
            e
            w
          
        
        =
        
          S
          
            o
            l
            d
          
        
        +
        
          
            
              
                (
                
                  5
                  −
                  T
                
                )
              
              
                2
              
            
            2
          
        
      
    
    {\displaystyle S_{new}=S_{old}+{\frac {\left(5-T\right)^{2}}{2}}}
  
{\displaystyle S_{new}=S_{old}+{\frac {\left(5-T\right)^{2}}{2}}}

<math>S_{new} = S_{old} +
 \frac{ \left( 5-T \right) ^2} {2}</math>

Integrals

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          ∫
          
            a
          
          
            x
          
        
        
          ∫
          
            a
          
          
            s
          
        
        f
        (
        y
        )
        
        d
        y
        
        d
        s
        =
        
          ∫
          
            a
          
          
            x
          
        
        f
        (
        y
        )
        (
        x
        −
        y
        )
        
        d
        y
      
    
    {\displaystyle \int _{a}^{x}\int _{a}^{s}f(y)\,dy\,ds=\int _{a}^{x}f(y)(x-y)\,dy}
  
{\displaystyle \int _{a}^{x}\int _{a}^{s}f(y)\,dy\,ds=\int _{a}^{x}f(y)(x-y)\,dy}

<math>\int_a^x \int_a^s f(y)\,dy\,ds
 = \int_a^x f(y)(x-y)\,dy</math>

Summation

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          ∑
          
            m
            =
            1
          
          
            ∞
          
        
        
          ∑
          
            n
            =
            1
          
          
            ∞
          
        
        
          
            
              
                m
                
                  2
                
              
              
              n
            
            
              
                3
                
                  m
                
              
              
                (
                
                  m
                  
                  
                    3
                    
                      n
                    
                  
                  +
                  n
                  
                  
                    3
                    
                      m
                    
                  
                
                )
              
            
          
        
      
    
    {\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}\,n}{3^{m}\left(m\,3^{n}+n\,3^{m}\right)}}}
  
{\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {m^{2}\,n}{3^{m}\left(m\,3^{n}+n\,3^{m}\right)}}}

<math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
 {3^m\left(m\,3^n+n\,3^m\right)}</math>

Differential Equation

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          u
          ″
        
        +
        p
        (
        x
        )
        
          u
          ′
        
        +
        q
        (
        x
        )
        u
        =
        f
        (
        x
        )
        ,
        
        x
        >
        a
      
    
    {\displaystyle u''+p(x)u'+q(x)u=f(x),\quad x>a}
  
{\displaystyle u''+p(x)u'+q(x)u=f(x),\quad x>a}

<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>

Complex numbers

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          |
        
        
          
            
              z
              ¯
            
          
        
        
          |
        
        =
        
          |
        
        z
        
          |
        
        ,
        
          |
        
        (
        
          
            
              z
              ¯
            
          
        
        
          )
          
            n
          
        
        
          |
        
        =
        
          |
        
        z
        
          
            |
          
          
            n
          
        
        ,
        arg
        ⁡
        (
        
          z
          
            n
          
        
        )
        =
        n
        arg
        ⁡
        (
        z
        )
      
    
    {\displaystyle |{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)}
  
{\displaystyle |{\bar {z}}|=|z|,|({\bar {z}})^{n}|=|z|^{n},\arg(z^{n})=n\arg(z)}

<math>|\bar{z}| = |z|,
 |(\bar{z})^n| = |z|^n,
 \arg(z^n) = n \arg(z)</math>

Limits

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          lim
          
            z
            →
            
              z
              
                0
              
            
          
        
        f
        (
        z
        )
        =
        f
        (
        
          z
          
            0
          
        
        )
      
    
    {\displaystyle \lim _{z\rightarrow z_{0}}f(z)=f(z_{0})}
  
{\displaystyle \lim _{z\rightarrow z_{0}}f(z)=f(z_{0})}

<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

Integral Equation

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          ϕ
          
            n
          
        
        (
        κ
        )
        =
        
          
            1
            
              4
              
                π
                
                  2
                
              
              
                κ
                
                  2
                
              
            
          
        
        
          ∫
          
            0
          
          
            ∞
          
        
        
          
            
              sin
              ⁡
              (
              κ
              R
              )
            
            
              κ
              R
            
          
        
        
          
            ∂
            
              ∂
              R
            
          
        
        
          [
          
            
              R
              
                2
              
            
            
              
                
                  ∂
                  
                    D
                    
                      n
                    
                  
                  (
                  R
                  )
                
                
                  ∂
                  R
                
              
            
          
          ]
        
        
        d
        R
      
    
    {\displaystyle \phi _{n}(\kappa )={\frac {1}{4\pi ^{2}\kappa ^{2}}}\int _{0}^{\infty }{\frac {\sin(\kappa R)}{\kappa R}}{\frac {\partial }{\partial R}}\left[R^{2}{\frac {\partial D_{n}(R)}{\partial R}}\right]\,dR}
  
{\displaystyle \phi _{n}(\kappa )={\frac {1}{4\pi ^{2}\kappa ^{2}}}\int _{0}^{\infty }{\frac {\sin(\kappa R)}{\kappa R}}{\frac {\partial }{\partial R}}\left[R^{2}{\frac {\partial D_{n}(R)}{\partial R}}\right]\,dR}

<math>\phi_n(\kappa) =
 \frac{1}{4\pi^2\kappa^2} \int_0^\infty
 \frac{\sin(\kappa R)}{\kappa R}
 \frac{\partial}{\partial R}
 \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math>

Example

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          ϕ
          
            n
          
        
        (
        κ
        )
        =
        0.033
        
          C
          
            n
          
          
            2
          
        
        
          κ
          
            −
            11
            
              /
            
            3
          
        
        ,
        
        
          
            1
            
              L
              
                0
              
            
          
        
        ≪
        κ
        ≪
        
          
            1
            
              l
              
                0
              
            
          
        
      
    
    {\displaystyle \phi _{n}(\kappa )=0.033C_{n}^{2}\kappa ^{-11/3},\quad {\frac {1}{L_{0}}}\ll \kappa \ll {\frac {1}{l_{0}}}}
  
{\displaystyle \phi _{n}(\kappa )=0.033C_{n}^{2}\kappa ^{-11/3},\quad {\frac {1}{L_{0}}}\ll \kappa \ll {\frac {1}{l_{0}}}}

<math>\phi_n(\kappa) = 
 0.033C_n^2\kappa^{-11/3},\quad
 \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

Continuation and cases

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        f
        (
        x
        )
        =
        
          
            {
            
              
                
                  1
                
                
                  −
                  1
                  ≤
                  x
                  <
                  0
                
              
              
                
                  
                    
                      1
                      2
                    
                  
                
                
                  x
                  =
                  0
                
              
              
                
                  1
                  −
                  
                    x
                    
                      2
                    
                  
                
                
                  0
                  <
                  x
                  ≤
                  1
                
              
            
            
          
        
      
    
    {\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&0<x\leq 1\end{cases}}}
  
{\displaystyle f(x)={\begin{cases}1&-1\leq x<0\\{\frac {1}{2}}&x=0\\1-x^{2}&0<x\leq 1\end{cases}}}

<math>
 f(x) =
 \begin{cases}
 1 & -1 \le x < 0 \\
 \frac{1}{2} & x = 0 \\
 1 - x^2 & 0 < x\le 1
 \end{cases}
 </math>

Prefixed subscript

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            p
          
        
        
          F
          
            q
          
        
        (
        
          a
          
            1
          
        
        ,
        …
        ,
        
          a
          
            p
          
        
        ;
        
          c
          
            1
          
        
        ,
        …
        ,
        
          c
          
            q
          
        
        ;
        z
        )
        =
        
          ∑
          
            n
            =
            0
          
          
            ∞
          
        
        
          
            
              (
              
                a
                
                  1
                
              
              
                )
                
                  n
                
              
              ⋅
              ⋅
              ⋅
              (
              
                a
                
                  p
                
              
              
                )
                
                  n
                
              
            
            
              (
              
                c
                
                  1
                
              
              
                )
                
                  n
                
              
              ⋅
              ⋅
              ⋅
              (
              
                c
                
                  q
                
              
              
                )
                
                  n
                
              
            
          
        
        
          
            
              z
              
                n
              
            
            
              n
              !
            
          
        
      
    
    {\displaystyle {}_{p}F_{q}(a_{1},\dots ,a_{p};c_{1},\dots ,c_{q};z)=\sum _{n=0}^{\infty }{\frac {(a_{1})_{n}\cdot \cdot \cdot (a_{p})_{n}}{(c_{1})_{n}\cdot \cdot \cdot (c_{q})_{n}}}{\frac {z^{n}}{n!}}}
  
{\displaystyle {}_{p}F_{q}(a_{1},\dots ,a_{p};c_{1},\dots ,c_{q};z)=\sum _{n=0}^{\infty }{\frac {(a_{1})_{n}\cdot \cdot \cdot (a_{p})_{n}}{(c_{1})_{n}\cdot \cdot \cdot (c_{q})_{n}}}{\frac {z^{n}}{n!}}}

 <math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
 = \sum_{n=0}^\infty
 \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}
 \frac{z^n}{n!}</math>

Bug reports

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Discussions, bug reports and feature requests should go to the Wikitech-l mailing list. These can also be filed on Mediazilla under MediaWiki extensions.

See also

[değiştir | kaynağı değiştir]
  • Typesetting of mathematical formulas
  • Proposed m:GNU LilyPond support
  • Table of mathematical symbols
  • m:Blahtex, or blahtex: a LaTeX to MathML converter for Wikipedia
  • General help for editing a Wiki page
  • Mimetex alternative for an another way to display mathematics using Mimetex.cgi

External links

[değiştir | kaynağı değiştir]
  • A LaTeX tutorial. http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/
  • A PDF document introducing TeX -- see page 39 onwards for a good introduction to the maths side of things: http://www.ctan.org/tex-archive/info/gentle/gentle.pdf
  • A PDF document introducing LaTeX -- skip to page 59 for the math section. See page 72 for a complete reference list of symbols included in LaTeX and AMS-LaTeX. http://www.ctan.org/tex-archive/info/lshort/english/lshort.pdf
  • TeX reference card: http://www.csit.fsu.edu/docs/tex/tex-refcard-letter.pdf
  • http://www.ams.org/tex/amslatex.html
  • A set of public domain fixed-size math symbol bitmaps: http://us.metamath.org/symbols/symbols.html
  • MathML - A product of the W3C Math working group, is a low-level specification for describing mathematics as a basis for machine to machine communication. http://www.w3.org/Math/
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