Matematiksel formüller

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Admin (Mesaj | katkılar) tarafından oluşturulmuş 13:39, 19 Şubat 2014 tarihli sürüm

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Atla: kullan, ara

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.


UNIQ0bd346bf6e656e70-item-541--QINU

Kodlama

Matematiksel kodlar UNIQ0bd346bf6e656e70-code-0000021E-QINU kodları arasına yazılır. Math markup goes inside UNIQ0bd346bf6e656e70-code-0000021F-QINU. The edit toolbar has a button for this.

UNIQ0bd346bf6e656e70-item-544--QINU Tex kodları doğru yazılmadıkları zaman hata uyarısı verirler. Bu nedenle kodları doğru yazdığınızdan emin olmalısınız.

UNIQ0bd346bf6e656e70-item-545--QINU

Sunum

UNIQ0bd346bf6e656e70-item-546--QINU It should be pointed out that most of these shortcomings have been addressed by Maynard Handley, but have not been released yet.

The UNIQ0bd346bf6e656e70-code-00000223-QINU 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 UNIQ0bd346bf6e656e70-code-00000224-QINU and UNIQ0bd346bf6e656e70-code-00000225-QINU.

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 UNIQ0bd346bf6e656e70-code-00000226-QINU or UNIQ0bd346bf6e656e70-code-00000227-QINU. For example, UNIQ0bd346bf6e656e70-code-00000228-QINU gives $ \mbox{abc} $.

TeX ve HTML

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
UNIQ0bd346bf6e656e70-code-00000229-QINU $ \alpha\, $ UNIQ0bd346bf6e656e70-code-0000022A-QINU α
UNIQ0bd346bf6e656e70-code-0000022B-QINU $ \sqrt{2} $ UNIQ0bd346bf6e656e70-code-0000022C-QINU √2
UNIQ0bd346bf6e656e70-code-0000022D-QINU $ \sqrt{1-e^2} $ UNIQ0bd346bf6e656e70-code-0000022E-QINU √1−e²</div>


UNIQ0bd346bf6e656e70-item-559--QINUas follows.

HTML'nin avantajları

  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

  1. Tex kalite bakımından HTML'den ileri bir yazılımdır.
  2. Tex yazılımında "UNIQ0bd346bf6e656e70-code-00000230-QINU" kodlaması matematiksel değişken anlamına gelir. Fakat HTML'de "UNIQ0bd346bf6e656e70-code-00000231-QINU" 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

UNIQ0bd346bf6e656e70-item-562--QINU{| class="wikitable"

! colspan="2" |

Aksanlar/Vurgular

|- |UNIQ0bd346bf6e656e70-code-00000233-QINU |$ \acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000234-QINU |$ \check{a} \bar{a} \ddot{a} \dot{a}\,\! $ |- ! colspan="2" |

Standart fonksiyonlar

|- |UNIQ0bd346bf6e656e70-code-00000235-QINU |$ \sin a \cos b \tan c\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000236-QINU |$ \sec d \csc e \cot f\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000237-QINU |$ \arcsin h \arccos i \arctan j\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000238-QINU |$ \sinh k \cosh l \tanh m \coth n\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000239-QINU |$ \operatorname{sh}o \operatorname{ch}p \operatorname{th}q\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000023A-QINU |$ \operatorname{argsh}r \operatorname{argch}s \operatorname{argth}t\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000023B-QINU |$ \lim u \limsup v \liminf w \min x \max y\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000023C-QINU |$ \inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000023D-QINU |$ \deg h \gcd i \Pr j \det k \hom l \arg m \dim n\,\! $ |-

! colspan="2" |

Modüler aritmatik

|- |UNIQ0bd346bf6e656e70-code-0000023E-QINU |$ s_k \equiv 0 \pmod{m} a \bmod b\,\! $ |- ! colspan="2" |

Türevsel karakterler

|- |UNIQ0bd346bf6e656e70-code-0000023F-QINU |$ \nabla \partial x dx \dot x \ddot y\,\! $ |- ! colspan="2" |

Kümeler

|- |UNIQ0bd346bf6e656e70-code-00000240-QINU |$ \forall \exists \empty \emptyset \varnothing\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000241-QINU |$ \in \ni \not \in \notin \subset \subseteq \supset \supseteq\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000242-QINU |$ \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000243-QINU |$ \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\! $ |- ! colspan="2" |

Operatör işaretler

|- |UNIQ0bd346bf6e656e70-code-00000244-QINU |$ + \oplus \bigoplus \pm \mp - \,\! $ |- |UNIQ0bd346bf6e656e70-code-00000245-QINU |$ \times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000246-QINU |$ \star * / \div \frac{1}{2}\,\! $ |- ! colspan="2" |

Mantıksal ifadeler

|- |UNIQ0bd346bf6e656e70-code-00000247-QINU |$ \land \wedge \bigwedge \bar{q} \to p\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000248-QINU |$ \lor \vee \bigvee \lnot \neg q \And\,\! $ |- ! colspan="2" |

Kök alma

|- |UNIQ0bd346bf6e656e70-code-00000249-QINU |$ \sqrt{2} \sqrt[n]{x}\,\! $ |- ! colspan="2" |

Eşitlik/Denklik/Benzerlik işaretleri

|- |UNIQ0bd346bf6e656e70-code-0000024A-QINU |$ \sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000024B-QINU |$ \le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto\,\! $ |- ! colspan="2" |

Geometrik

|- |UNIQ0bd346bf6e656e70-code-0000024C-QINU |$ \Diamond \, \Box \, \triangle \, \angle \perp \, \mid \; \nmid \, \| 45^\circ\,\! $ |- ! colspan="2" |

Oklar/Bildiri ifadeleri

|- |UNIQ0bd346bf6e656e70-code-0000024D-QINU |$ \leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000024E-QINU |$ \mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000024F-QINU |$ \uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000250-QINU |$ \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000251-QINU |$ \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\! $ |- |UNIQ0bd346bf6e656e70-code-00000252-QINU |$ \leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000253-QINU |$ \curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000254-QINU |$ \nLeftrightarrow \longleftrightarrow\,\! $ |-

! colspan="2" |

Özel

|- |UNIQ0bd346bf6e656e70-code-00000255-QINU |$ \eth \S \P \% \dagger \ddagger \ldots \cdots\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000256-QINU |$ \smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000257-QINU |$ \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000258-QINU |$ \ell \mho \Finv \Re \Im \wp \complement \diamondsuit\,\! $ |- |UNIQ0bd346bf6e656e70-code-00000259-QINU |$ \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\! $ |- ! colspan="2" |

Unsorted (new stuff)

|- |UNIQ0bd346bf6e656e70-code-0000025A-QINU |$ \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown $ |- |UNIQ0bd346bf6e656e70-code-0000025B-QINU |$ \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge $ |- |UNIQ0bd346bf6e656e70-code-0000025C-QINU |$ \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes $ |- |UNIQ0bd346bf6e656e70-code-0000025D-QINU |$ \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant $ |- |UNIQ0bd346bf6e656e70-code-0000025E-QINU |$ \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq $ |- |UNIQ0bd346bf6e656e70-code-0000025F-QINU |$ \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft $ |- |UNIQ0bd346bf6e656e70-code-00000260-QINU |$ \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot $ |- |UNIQ0bd346bf6e656e70-code-00000261-QINU |$ \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq $ |- |UNIQ0bd346bf6e656e70-code-00000262-QINU |$ \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork $ |- |UNIQ0bd346bf6e656e70-code-00000263-QINU |$ \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq $ |- |UNIQ0bd346bf6e656e70-code-00000264-QINU |$ \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid $ |- |UNIQ0bd346bf6e656e70-code-00000265-QINU |$ \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr $ |- |UNIQ0bd346bf6e656e70-code-00000266-QINU |$ \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq $ |- |UNIQ0bd346bf6e656e70-code-00000267-QINU |$ \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq $ |- |UNIQ0bd346bf6e656e70-code-00000268-QINU |$ \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq $ |- |UNIQ0bd346bf6e656e70-code-00000269-QINU |$ \jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000026A-QINU |$ \oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,\! $ |- |UNIQ0bd346bf6e656e70-code-0000026B-QINU |$ \dashv \asymp \doteq \parallel\,\! $ |}

Üslü ifadeler, toplam-çarpım sembolleri, türev, integral

Feature Syntax How it looks rendered
HTML PNG
Superscript UNIQ0bd346bf6e656e70-code-0000026C-QINU $ a^2 $ $ a^2 \,\! $
Subscript UNIQ0bd346bf6e656e70-code-0000026D-QINU $ a_2 $ $ a_2 \,\! $
Grouping UNIQ0bd346bf6e656e70-code-0000026E-QINU $ a^{2+2} $ $ a^{2+2}\,\! $
UNIQ0bd346bf6e656e70-code-0000026F-QINU $ a_{i,j} $ $ a_{i,j}\,\! $
Combining sub & super UNIQ0bd346bf6e656e70-code-00000270-QINU $ x_2^3 $
Preceding and/or Additional sub & super UNIQ0bd346bf6e656e70-code-00000271-QINU $ \sideset{_1^2}{_3^4}\prod_a^b $
UNIQ0bd346bf6e656e70-code-00000272-QINU $ {}_1^2\!\Omega_3^4 $
Stacking UNIQ0bd346bf6e656e70-code-00000273-QINU $ \overset{\alpha}{\omega} $
UNIQ0bd346bf6e656e70-code-00000274-QINU $ \underset{\alpha}{\omega} $
UNIQ0bd346bf6e656e70-code-00000275-QINU $ \overset{\alpha}{\underset{\gamma}{\omega}} $
UNIQ0bd346bf6e656e70-code-00000276-QINU $ \stackrel{\alpha}{\omega} $
Derivative (forced PNG) UNIQ0bd346bf6e656e70-code-00000277-QINU   $ x', y'', f', f''\! $
Derivative (f in italics may overlap primes in HTML) UNIQ0bd346bf6e656e70-code-00000278-QINU $ x', y'', f', f'' $ $ x', y'', f', f''\! $
Derivative (HTML-yanlış) UNIQ0bd346bf6e656e70-code-00000279-QINU $ x^\prime, y^{\prime\prime} $ $ x^\prime, y^{\prime\prime}\,\! $
Derivative (PNG-yanlış) UNIQ0bd346bf6e656e70-code-0000027A-QINU $ x\prime, y\prime\prime $ $ x\prime, y\prime\prime\,\! $
Derivative dots UNIQ0bd346bf6e656e70-code-0000027B-QINU $ \dot{x}, \ddot{x} $
Underlines, overlines, vectors UNIQ0bd346bf6e656e70-code-0000027C-QINU $ \hat a \ \bar b \ \vec c $
UNIQ0bd346bf6e656e70-code-0000027D-QINU $ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} $
UNIQ0bd346bf6e656e70-code-0000027E-QINU $ \overline{g h i} \ \underline{j k l} $
Arrows UNIQ0bd346bf6e656e70-code-0000027F-QINU $ A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C $
Overbraces UNIQ0bd346bf6e656e70-code-00000280-QINU $ \overbrace{ 1+2+\cdots+100 }^{5050} $
Underbraces UNIQ0bd346bf6e656e70-code-00000281-QINU $ \underbrace{ a+b+\cdots+z }_{26} $
Sum UNIQ0bd346bf6e656e70-code-00000282-QINU $ \sum_{k=1}^N k^2 $
Sum (force UNIQ0bd346bf6e656e70-code-00000283-QINU) UNIQ0bd346bf6e656e70-code-00000284-QINU $ \textstyle \sum_{k=1}^N k^2 $
Product UNIQ0bd346bf6e656e70-code-00000285-QINU $ \prod_{i=1}^N x_i $
Product (force UNIQ0bd346bf6e656e70-code-00000286-QINU) UNIQ0bd346bf6e656e70-code-00000287-QINU $ \textstyle \prod_{i=1}^N x_i $
Coproduct UNIQ0bd346bf6e656e70-code-00000288-QINU $ \coprod_{i=1}^N x_i $
Coproduct (force UNIQ0bd346bf6e656e70-code-00000289-QINU) UNIQ0bd346bf6e656e70-code-0000028A-QINU $ \textstyle \coprod_{i=1}^N x_i $
Limit UNIQ0bd346bf6e656e70-code-0000028B-QINU $ \lim_{n \to \infty}x_n $
Limit (force UNIQ0bd346bf6e656e70-code-0000028C-QINU) UNIQ0bd346bf6e656e70-code-0000028D-QINU $ \textstyle \lim_{n \to \infty}x_n $
Integral UNIQ0bd346bf6e656e70-code-0000028E-QINU $ \int_{-N}^{N} e^x\, dx $
İntegral (force UNIQ0bd346bf6e656e70-code-0000028F-QINU) UNIQ0bd346bf6e656e70-code-00000290-QINU $ \textstyle \int_{-N}^{N} e^x\, dx $
Çift katlı integral UNIQ0bd346bf6e656e70-code-00000291-QINU $ \iint_{D}^{W} \, dx\,dy $
Üç katlı integral UNIQ0bd346bf6e656e70-code-00000292-QINU $ \iiint_{E}^{V} \, dx\,dy\,dz $
Dört katlı integral UNIQ0bd346bf6e656e70-code-00000293-QINU $ \iiiint_{F}^{U} \, dx\,dy\,dz\,dt $
Path integral UNIQ0bd346bf6e656e70-code-00000294-QINU $ \oint_{C} x^3\, dx + 4y^2\, dy $
Intersections UNIQ0bd346bf6e656e70-code-00000295-QINU $ \bigcap_1^{n} p $
Unions UNIQ0bd346bf6e656e70-code-00000296-QINU $ \bigcup_1^{k} p $

Fractions, matrices, multilines

Feature Syntax How it looks rendered
Fractions UNIQ0bd346bf6e656e70-code-00000297-QINU $ \frac{2}{4}=0.5 $
Small Fractions UNIQ0bd346bf6e656e70-code-00000298-QINU $ \tfrac{2}{4} = 0.5 $
Large (normal) Fractions UNIQ0bd346bf6e656e70-code-00000299-QINU $ \dfrac{2}{4} = 0.5 $
Large (nestled) Fractions UNIQ0bd346bf6e656e70-code-0000029A-QINU $ \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a $
Binomial coefficients UNIQ0bd346bf6e656e70-code-0000029B-QINU $ \binom{n}{k} $
Small Binomial coefficients UNIQ0bd346bf6e656e70-code-0000029C-QINU $ \tbinom{n}{k} $
Large (normal) Binomial coefficients UNIQ0bd346bf6e656e70-code-0000029D-QINU $ \dbinom{n}{k} $
Matrices UNIQ0bd346bf6e656e70-pre-0000029E-QINU $ \begin{matrix} x & y \\ z & v \end{matrix} $
UNIQ0bd346bf6e656e70-pre-0000029F-QINU $ \begin{vmatrix} x & y \\ z & v \end{vmatrix} $
UNIQ0bd346bf6e656e70-pre-000002A0-QINU $ \begin{Vmatrix} x & y \\ z & v \end{Vmatrix} $
UNIQ0bd346bf6e656e70-pre-000002A1-QINU $ \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} $
UNIQ0bd346bf6e656e70-pre-000002A2-QINU $ \begin{Bmatrix} x & y \\ z & v \end{Bmatrix} $
UNIQ0bd346bf6e656e70-pre-000002A3-QINU $ \begin{pmatrix} x & y \\ z & v \end{pmatrix} $
UNIQ0bd346bf6e656e70-pre-000002A4-QINU $ \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) $
Case distinctions UNIQ0bd346bf6e656e70-pre-000002A5-QINU $ f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} $
Multiline equations UNIQ0bd346bf6e656e70-pre-000002A6-QINU $ \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} $
UNIQ0bd346bf6e656e70-pre-000002A7-QINU $ \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} $
Multiline equations (must define number of colums used ({lcr}) (should not be used unless needed) UNIQ0bd346bf6e656e70-pre-000002A8-QINU $ \begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array} $
Multiline equations (more) UNIQ0bd346bf6e656e70-pre-000002A9-QINU $ \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 UNIQ0bd346bf6e656e70-pre-000002AA-QINU

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

Simultaneous equations UNIQ0bd346bf6e656e70-pre-000002AB-QINU $ \begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases} $

Alphabets and typefaces

Greek alphabet
UNIQ0bd346bf6e656e70-code-000002AC-QINU $ \Alpha \Beta \Gamma \Delta \Epsilon \Zeta \,\! $
UNIQ0bd346bf6e656e70-code-000002AD-QINU $ \Eta \Theta \Iota \Kappa \Lambda \Mu \,\! $
UNIQ0bd346bf6e656e70-code-000002AE-QINU $ \Nu \Xi \Pi \Rho \Sigma \Tau\,\! $
UNIQ0bd346bf6e656e70-code-000002AF-QINU $ \Upsilon \Phi \Chi \Psi \Omega \,\! $
UNIQ0bd346bf6e656e70-code-000002B0-QINU $ \alpha \beta \gamma \delta \epsilon \zeta \,\! $
UNIQ0bd346bf6e656e70-code-000002B1-QINU $ \eta \theta \iota \kappa \lambda \mu \,\! $
UNIQ0bd346bf6e656e70-code-000002B2-QINU $ \nu \xi \pi \rho \sigma \tau \,\! $
UNIQ0bd346bf6e656e70-code-000002B3-QINU $ \upsilon \phi \chi \psi \omega \,\! $
UNIQ0bd346bf6e656e70-code-000002B4-QINU $ \varepsilon \digamma \vartheta \varkappa \,\! $
UNIQ0bd346bf6e656e70-code-000002B5-QINU $ \varpi \varrho \varsigma \varphi\,\! $
Blackboard Bold/Scripts
UNIQ0bd346bf6e656e70-code-000002B6-QINU $ \mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} \,\! $
UNIQ0bd346bf6e656e70-code-000002B7-QINU $ \mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} \,\! $
UNIQ0bd346bf6e656e70-code-000002B8-QINU $ \mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} \,\! $
UNIQ0bd346bf6e656e70-code-000002B9-QINU $ \mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}\,\! $
boldface (vectors)
UNIQ0bd346bf6e656e70-code-000002BA-QINU $ \mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} \,\! $
UNIQ0bd346bf6e656e70-code-000002BB-QINU $ \mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} \,\! $
UNIQ0bd346bf6e656e70-code-000002BC-QINU $ \mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} \,\! $
UNIQ0bd346bf6e656e70-code-000002BD-QINU $ \mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} \,\! $
UNIQ0bd346bf6e656e70-code-000002BE-QINU $ \mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} \,\! $
UNIQ0bd346bf6e656e70-code-000002BF-QINU $ \mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} \,\! $
UNIQ0bd346bf6e656e70-code-000002C0-QINU $ \mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} \,\! $
UNIQ0bd346bf6e656e70-code-000002C1-QINU $ \mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} \,\! $
UNIQ0bd346bf6e656e70-code-000002C2-QINU $ \mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} \,\! $
UNIQ0bd346bf6e656e70-code-000002C3-QINU $ \mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}\,\! $
Boldface (greek)
UNIQ0bd346bf6e656e70-code-000002C4-QINU $ \boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} \,\! $
UNIQ0bd346bf6e656e70-code-000002C5-QINU $ \boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}\,\! $
UNIQ0bd346bf6e656e70-code-000002C6-QINU $ \boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}\,\! $
UNIQ0bd346bf6e656e70-code-000002C7-QINU $ \boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}\,\! $
UNIQ0bd346bf6e656e70-code-000002C8-QINU $ \boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}\,\! $
UNIQ0bd346bf6e656e70-code-000002C9-QINU $ \boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}\,\! $
UNIQ0bd346bf6e656e70-code-000002CA-QINU $ \boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}\,\! $
UNIQ0bd346bf6e656e70-code-000002CB-QINU $ \boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}\,\! $
UNIQ0bd346bf6e656e70-code-000002CC-QINU $ \boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} \,\! $
UNIQ0bd346bf6e656e70-code-000002CD-QINU $ \boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}\,\! $
Italics
UNIQ0bd346bf6e656e70-code-000002CE-QINU $ \mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} \,\! $
UNIQ0bd346bf6e656e70-code-000002CF-QINU $ \mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} \,\! $
UNIQ0bd346bf6e656e70-code-000002D0-QINU $ \mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} \,\! $
UNIQ0bd346bf6e656e70-code-000002D1-QINU $ \mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} \,\! $
UNIQ0bd346bf6e656e70-code-000002D2-QINU $ \mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} \,\! $
UNIQ0bd346bf6e656e70-code-000002D3-QINU $ \mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} \,\! $
UNIQ0bd346bf6e656e70-code-000002D4-QINU $ \mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} \,\! $
UNIQ0bd346bf6e656e70-code-000002D5-QINU $ \mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} \,\! $
UNIQ0bd346bf6e656e70-code-000002D6-QINU $ \mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} \,\! $
UNIQ0bd346bf6e656e70-code-000002D7-QINU $ \mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}\,\! $
Roman typeface
UNIQ0bd346bf6e656e70-code-000002D8-QINU $ \mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} \,\! $
UNIQ0bd346bf6e656e70-code-000002D9-QINU $ \mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} \,\! $
UNIQ0bd346bf6e656e70-code-000002DA-QINU $ \mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} \,\! $
UNIQ0bd346bf6e656e70-code-000002DB-QINU $ \mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} \,\! $
UNIQ0bd346bf6e656e70-code-000002DC-QINU $ \mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}\,\! $
UNIQ0bd346bf6e656e70-code-000002DD-QINU $ \mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} \,\! $
UNIQ0bd346bf6e656e70-code-000002DE-QINU $ \mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} \,\! $
UNIQ0bd346bf6e656e70-code-000002DF-QINU $ \mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} \,\! $
UNIQ0bd346bf6e656e70-code-000002E0-QINU $ \mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} \,\! $
UNIQ0bd346bf6e656e70-code-000002E1-QINU $ \mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}\,\! $
Fraktur typeface
UNIQ0bd346bf6e656e70-code-000002E2-QINU $ \mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} \,\! $
UNIQ0bd346bf6e656e70-code-000002E3-QINU $ \mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} \,\! $
UNIQ0bd346bf6e656e70-code-000002E4-QINU $ \mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} \,\! $
UNIQ0bd346bf6e656e70-code-000002E5-QINU $ \mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} \,\! $
UNIQ0bd346bf6e656e70-code-000002E6-QINU $ \mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} \,\! $
UNIQ0bd346bf6e656e70-code-000002E7-QINU $ \mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} \,\! $
UNIQ0bd346bf6e656e70-code-000002E8-QINU $ \mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} \,\! $
UNIQ0bd346bf6e656e70-code-000002E9-QINU $ \mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} \,\! $
UNIQ0bd346bf6e656e70-code-000002EA-QINU $ \mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} \,\! $
UNIQ0bd346bf6e656e70-code-000002EB-QINU $ \mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}\,\! $
Calligraphy/Script
UNIQ0bd346bf6e656e70-code-000002EC-QINU $ \mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} \,\! $
UNIQ0bd346bf6e656e70-code-000002ED-QINU $ \mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} \,\! $
UNIQ0bd346bf6e656e70-code-000002EE-QINU $ \mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} \,\! $
UNIQ0bd346bf6e656e70-code-000002EF-QINU $ \mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}\,\! $
Hebrew
UNIQ0bd346bf6e656e70-code-000002F0-QINU $ \aleph \beth \gimel \daleth\,\! $
Feature Syntax How it looks rendered
non-italicised characters \mbox{abc} $ \mbox{abc} $ $ \mbox{abc} \,\! $
mixed italics (bad) \mbox{if} n \mbox{is even} $ \mbox{if} n \mbox{is even} $ $ \mbox{if} n \mbox{is even} \,\! $
mixed italics (good) \mbox{if }n\mbox{ is even} $ \mbox{if }n\mbox{ is even} $ $ \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} $ \mbox{if}~n\ \mbox{is even} $ $ \mbox{if}~n\ \mbox{is even} \,\! $

Parenthesizing big expressions, brackets, bars

Feature Syntax How it looks rendered
Bad ( \frac{1}{2} ) $ ( \frac{1}{2} ) $
Good \left ( \frac{1}{2} \right ) $ \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 ) $ \left ( \frac{a}{b} \right ) $
Brackets \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack $ \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 $ \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace $
Angle brackets \left \langle \frac{a}{b} \right \rangle $ \left \langle \frac{a}{b} \right \rangle $
Bars and double bars \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \| $ \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 $ \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil $
Slashes and backslashes \left / \frac{a}{b} \right \backslash $ \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 $ \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 |

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

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

$ \big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big] $

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

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

\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big| $ \big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big| $
\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil

$ \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

$ \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

$ \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

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

Spacing

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 \qquad b $
quad space a \quad b $ a \quad b $
text space a\ b $ a\ b $
text space without PNG conversion a \mbox{ } b $ a \mbox{ } b $
large space a\;b $ a\;b $
medium space a\>b [not supported]
small space a\,b $ a\,b $
no space ab $ ab\, $
small negative space a\!b $ a\!b $

Align with normal text flow

Due to the default css

UNIQ0bd346bf6e656e70-pre-000002F1-QINU

an inline expression like $ \int_{-N}^{N} e^x\, dx = 2 \sinh N $ should look good.

If you need to align it otherwise, use UNIQ0bd346bf6e656e70-code-000002F2-QINU and play with the UNIQ0bd346bf6e656e70-code-000002F3-QINU 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

To force the formula to render as PNG, add UNIQ0bd346bf6e656e70-code-000002F4-QINU (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 UNIQ0bd346bf6e656e70-code-000002F5-QINU (small space and negative space, which cancel out) anywhere inside the math tags. This does force PNG even in "HTML if possible" mode, unlike UNIQ0bd346bf6e656e70-code-000002F6-QINU.

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} $
a^{c+2} \, $ a^{c+2} \, $
a^{\,\!c+2} $ a^{\,\!c+2} $
a^{b^{c+2}} $ a^{b^{c+2}} $ (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}} \, $ a^{b^{c+2}} \, $ (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}}\approx 5 $ a^{b^{c+2}}\approx 5 $ (due to "$ \approx $" correctly displayed, no code "\,\!" needed)
a^{b^{\,\!c+2}} $ a^{b^{\,\!c+2}} $
\int_{-N}^{N} e^x\, dx $ \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:

UNIQ0bd346bf6e656e70-nowiki-000002F7-QINU

Color

Equations can use color:

  • UNIQ0bd346bf6e656e70-code-000002F8-QINU
    $ {\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1} $
  • UNIQ0bd346bf6e656e70-code-000002F9-QINU
    $ 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 en:Wikipedia:Manual of Style#Formatting issues.

Examples

Quadratic Polynomial

$ ax^2 + bx + c = 0 $

UNIQ0bd346bf6e656e70-nowiki-000002FA-QINU

Quadratic Polynomial (Force PNG Rendering)

$ ax^2 + bx + c = 0\,\! $

UNIQ0bd346bf6e656e70-nowiki-000002FB-QINU

Quadratic Formula

$ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} $

UNIQ0bd346bf6e656e70-nowiki-000002FC-QINU

Tall Parentheses and Fractions

$ 2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right) $

UNIQ0bd346bf6e656e70-nowiki-000002FD-QINU

$ S_{new} = S_{old} + \frac{ \left( 5-T \right) ^2} {2} $

UNIQ0bd346bf6e656e70-nowiki-000002FE-QINU

Integrals

$ \int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy $

UNIQ0bd346bf6e656e70-nowiki-000002FF-QINU

Summation

$ \sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)} $

UNIQ0bd346bf6e656e70-nowiki-00000300-QINU

Differential Equation

$ u'' + p(x)u' + q(x)u=f(x),\quad x>a $

UNIQ0bd346bf6e656e70-nowiki-00000301-QINU

Complex numbers

$ |\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z) $

UNIQ0bd346bf6e656e70-nowiki-00000302-QINU

Limits

$ \lim_{z\rightarrow z_0} f(z)=f(z_0) $

UNIQ0bd346bf6e656e70-nowiki-00000303-QINU

Integral Equation

$ \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 $

UNIQ0bd346bf6e656e70-nowiki-00000304-QINU

Example

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

UNIQ0bd346bf6e656e70-nowiki-00000305-QINU

Continuation and cases

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

UNIQ0bd346bf6e656e70-nowiki-00000306-QINU

Prefixed subscript

$ {}_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!} $

UNIQ0bd346bf6e656e70-nowiki-00000307-QINU

Bug reports

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

External links

"http://www.turkmath.org/w/index.php?title=Matematiksel_formüller&oldid=68" adresinden alındı.