Hjálp:Hvernig set ég inn stærðfræði formúlur?

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ISIRWiki notar TeX tungumálið fyrir stærðfræði formúlur.

--Freysteinn 20:41, 14. október 2005 (GMT) Þessi hjálparsíða er ekki tilbúin. Vonandi koma töflurnar samt að gagni.

--Freysteinn 20:41, 14. október 2005 (GMT) Þessi síða verður þýdd yfir á íslensku, og breytt tölvert, þar sem sumar töflurnar eru ekki nóg vel upp settar.

--Freysteinn 20:41, 14. október 2005 (GMT) Til þess að setja stærðfræði formúlu á síðu, setjið <math> stærðfræði skipanir</math>. Skipaninar eru flestar í töflunum hérna fyrir neðan.

Feature Syntax rendered
Accents/Diacritics \acute{a} \quad \grave{a} \quad \breve{a} \quad \check{a} \quad \tilde{a} <math>\acute{a} \quad \grave{a} \quad \breve{a} \quad \check{a} \quad \tilde{a}</math>
Std. functions (good) \sin x + \ln y +\operatorname{sgn} z

\sin a \ \cos b \ \tan c \ \cot d \ \sec e \ \csc f
\sinh g \ \cosh h \ \tanh i \ \coth j
\arcsin k \ \arccos l \ \arctan m
\lim n \ \limsup o \ \liminf p
\min q \ \max r \ \inf s \ \sup t
\exp u \ \lg v \ \log w
\ker x \ \deg x \gcd x \Pr x \ \det x \hom x \ \arg x \dim x

<math>\sin x + \ln y +\operatorname{sgn} z</math>

<math>\sin a \ \cos b \ \tan c \ \cot d \ \sec e \ \csc f</math>
<math>\sinh g \ \cosh h \ \tanh i \ \coth j</math>
<math>\arcsin k \ \arccos l \ \arctan m</math>
<math>\lim n \ \limsup o \ \liminf p</math>
<math>\min q \ \max r \ \inf s \ \sup t</math>
<math>\exp u \ \lg v \ \log w</math>
<math>\ker x \ \deg x \gcd x \Pr x \ \det x \hom x \ \arg x \dim x</math>

Std. functions (wrong) sin x + ln y + sgn z <math>sin x + ln y + sgn z\,\!</math>
Modular arithmetic s_k \equiv 0 \pmod{m}

a \bmod b

<math>s_k \equiv 0 \pmod{m}</math>

<math>a \bmod b\,\!</math>

Derivatives \nabla \; \partial x \; dx \; \dot x \; \ddot y <math>\nabla \; \partial x \; dx \; \dot x \; \ddot y</math>
Sets

(Square symbols may not work for some wikis)

\forall \; \exists \; \empty \; \emptyset \; \varnothing \in \ni \not\in \notin

\subset \subseteq \supset \supseteq \cap \bigcap \cup \bigcup \biguplus

<math>\forall \; \exists \; \empty \; \emptyset \; \varnothing \in \ni \not\in \notin</math>

<math>\subset \subseteq \supset \supseteq \cap \bigcap \cup \bigcup \biguplus</math>

\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup <math>\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup</math>
Logic p \land \wedge \; \bigwedge \; \bar{q} \to p\ lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus <math>p \land \wedge \; \bigwedge \; \bar{q} \to p \lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus</math>
Root \sqrt{2}\approx 1.4 <math>\sqrt{2}\approx 1.4</math>
\sqrt[n]{x} <math>\sqrt[n]{x}</math>
Relations \sim \; \approx \; \simeq \; \cong \; \le \; < \; \ge \; > \; \equiv \; \not\equiv \; \ne \; \propto \; \pm \; \mp <math>\sim \; \approx \; \simeq \; \cong \; \le \; < \; \ge \; > \; \equiv \; \not\equiv \; \ne \; \propto \; \pm \; \mp</math>
Geometric \Diamond \; \Box \; \triangle \; \angle \; \perp \; \mid \; \nmid \; \| \; 45^\circ \; 45^\circ</math>
Arrows

(Harpoons may not work for some wikis)

\leftarrow \; \gets \; \rightarrow \; \to \; \leftrightarrow

\longleftarrow \; \longrightarrow
\mapsto \; \longmapsto \; \hookrightarrow \; \hookleftarrow
\nearrow \; \searrow \; \swarrow \; \nwarrow
\uparrow \; \downarrow \; \updownarrow

<math>\leftarrow \; \gets \; \rightarrow \; \to \; \leftrightarrow</math>

<math>\longleftarrow \; \longrightarrow</math>
<math>\mapsto \; \longmapsto \; \hookrightarrow \; \hookleftarrow</math>
<math>\nearrow \; \searrow \; \swarrow \; \nwarrow</math>
<math>\uparrow \; \downarrow \; \updownarrow</math>

\rightharpoonup \; \rightharpoondown \; \leftharpoonup \; \leftharpoondown \; \upharpoonleft \; \upharpoonright \; \downharpoonleft \; \downharpoonright <math>\rightharpoonup \; \rightharpoondown \; \leftharpoonup \; \leftharpoondown \; \upharpoonleft \; \upharpoonright \; \downharpoonleft \; \downharpoonright</math>
\Leftarrow \; \Rightarrow \; \Leftrightarrow

\Longleftarrow \; \Longrightarrow \; \Longleftrightarrow (or \iff)
\Uparrow \; \Downarrow \; \Updownarrow

<math>\Leftarrow \; \Rightarrow \; \Leftrightarrow</math>

<math>\Longleftarrow \; \Longrightarrow \; \Longleftrightarrow (or \iff)</math>
<math>\Uparrow \; \Downarrow \; \Updownarrow</math>

Special \eth \; \S \; \P \; \% \; \dagger \; \ddagger \; \star \; * \; \ldots

\smile \frown \wr \oplus \bigoplus \otimes \bigotimes
\times \cdot \circ \bullet \bigodot \triangleleft \triangleright \infty \bot \top \vdash \vDash \Vdash \models \lVert \rVert
\imath \; \hbar \; \ell \; \mho \; \Finv \; \Re \; \Im \; \wp \; \complement \quad \diamondsuit \; \heartsuit \; \clubsuit \; \spadesuit \; \Game \quad \flat \; \natural \; \sharp

<math>\eth \; \S \; \P \; \% \; \dagger \; \ddagger \; \star \; * \; \ldots</math>

<math>\smile \frown \wr \oplus \bigoplus \otimes \bigotimes</math>
<math>\times \cdot \circ \bullet \bigodot \triangleleft \triangleright \infty \bot \top \vdash \vDash \Vdash \models \lVert \rVert</math>
<math>\imath \; \hbar \; \ell \; \mho \; \Finv \; \Re \; \Im \; \wp \; \complement \quad \diamondsuit \; \heartsuit \; \clubsuit \; \spadesuit \; \Game \quad \flat \; \natural \; \sharp</math>

Lowercase \mathcal has some extras \mathcal {45abcdenpqstuvwx} <math>\mathcal {45abcdenpqstuvwx}</math>

Efnisyfirlit

[breyta] Subscripts, superscripts, integrals

Feature Syntax How it looks rendered
HTML PNG
Superscript a^2 <math>a^2</math> <math>a^2 \,\!</math>
Subscript a_2 <math>a_2</math> <math>a_2 \,\!</math>
Grouping a^{2+2} <math>a^{2+2}</math> <math>a^{2+2}\,\!</math>
a_{i,j} <math>a_{i,j}</math> <math>a_{i,j}\,\!</math>
Combining sub & super x_2^3 <math>x_2^3</math>
Preceding sub & super {}_1^2\!X_3^4 <math>{}_1^2\!X_3^4</math>
Derivative (good) x', y'' <math>x', y</math> <math>x', y\,\!</math>
Derivative (wrong in HTML) x^\prime, y^{\prime\prime} <math>x^\prime, y^{\prime\prime}</math> <math>x^\prime, y^{\prime\prime}\,\!</math>
Derivative (wrong in PNG) x\prime, y\prime\prime <math>x\prime, y\prime\prime</math> <math>x\prime, y\prime\prime\,\!</math>
Derivative dots \dot{x}, \ddot{x} <math>\dot{x}, \ddot{x}</math>
Underlines, overlines, vectors \hat a \ \bar b \ \vec c \ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} \ \overline{g h i} \ \underline{j k l} <math>\hat a \ \bar b \ \vec c \ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} \ \overline{g h i} \ \underline{j k l}</math>
Overbraces

\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}

<math>\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}</math>

Underbraces

\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}

<math>\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}</math>

Sum \sum_{k=1}^N k^2 <math>\sum_{k=1}^N k^2</math>
Product \prod_{i=1}^N x_i <math>\prod_{i=1}^N x_i</math>
Coproduct \coprod_{i=1}^N x_i <math>\coprod_{i=1}^N x_i</math>
Limit \lim_{n \to \infty}x_n <math>\lim_{n \to \infty}x_n</math>
Integral \int_{-N}^{N} e^x\, dx <math>\int_{-N}^{N} e^x\, dx</math>
Double integral \iint_{D}^{W} \, dx\,dy <math>\iint_{D}^{W} \, dx\,dy</math>
Triple integral \iiint_{E}^{V} \, dx\,dy\,dz <math>\iiint_{E}^{V} \, dx\,dy\,dz</math>
Quadruple integral \iiiint_{F}^{U} \, dx\,dy\,dz\,dt <math>\iiiint_{F}^{U} \, dx\,dy\,dz\,dt</math>
Path integral \oint_{C} x^3\, dx + 4y^2\, dy <math>\oint_{C} x^3\, dx + 4y^2\, dy</math>
Intersections \bigcap_1^{n} p <math>\bigcap_1^{n} p</math>
Unions \bigcup_1^{k} p <math>\bigcup_1^{k} p</math>

[breyta] Fractions, matrices, multilines

Feature Syntax How it looks rendered
Fractions \frac{2}{4} or {2 \over 4} <math>\frac{2}{4}</math>
Binomial coefficients {n \choose k} <math>{n \choose k}</math>
Small Fractions \begin{matrix} \frac{2}{4} \end{matrix} <math>\begin{matrix} \frac{2}{4} \end{matrix}</math>
Matrices \begin{matrix} x & y \\ z & v \end{matrix} <math>\begin{matrix} x & y \\ z & v \end{matrix}</math>
\begin{vmatrix} x & y \\ z & v \end{vmatrix} <math>\begin{vmatrix} x & y \\ z & v \end{vmatrix}</math>
\begin{Vmatrix} x & y \\ z & v \end{Vmatrix} <math>\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}</math>
\begin{bmatrix} 0 & \cdots & 0 \\ \vdots &

\ddots & \vdots \\ 0 & \cdots &

0\end{bmatrix}		 <math>\begin{bmatrix} 0 & \cdots & 0 \\ \vdots

& \ddots & \vdots \\ 0 & \cdots &

0\end{bmatrix} </math>
\begin{Bmatrix} x & y \\ z & v \end{Bmatrix} <math>\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}</math>
\begin{pmatrix} x & y \\ z & v \end{pmatrix} <math>\begin{pmatrix} x & y \\ z & v \end{pmatrix}</math>
Case distinctions f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} <math>f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} </math>
Multiline equations \begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix} <math>\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}</math>
Alternative multiline equations (using tables) 

{|
|-
|<math>f(n+1)</math>
|<math>=(n+1)^2</math>
|-
|
|<math>=n^2 + 2n + 1</math>
|}
<math>f(n+1) \,\!</math> <math>=(n+1)^2 \,\!</math>
<math>=n^2 + 2n + 1 \,\!</math>

[breyta] Fonts

Feature Syntax How it looks rendered
Greek alphabet
(Note the lack of omicron; note also that several upper case Greek letters are rendered identically to the corresponding Roman ones)

\Alpha\ \Beta\ \Gamma\ \Delta\ \Epsilon\ \Zeta\ \Eta\ \Theta\ \Iota\ \Kappa\ \Lambda\ \Mu\ \Nu\ \Xi\ \Pi\ \Rho\ \Sigma\ \Tau\ \Upsilon\ \Phi\ \Chi\ \Psi\ \Omega

\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega

\varepsilon\ \digamma\ \vartheta\ \varkappa\ \varpi\ \varrho\ \varsigma\ \varphi

<math>\Alpha\ \Beta\ \Gamma\ \Delta\ \Epsilon\ \Zeta\ \Eta\ \Theta\ \Iota\ \Kappa\ \Lambda\ \Mu\ \Nu\ \Xi\ \Pi\ \Rho\ \Sigma\ \Tau\ \Upsilon\ \Phi\ \Chi\ \Psi\ \Omega</math>

<math>\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega</math>

<math>\varepsilon\ \digamma\ \vartheta\ \varkappa\ \varpi\ \varrho\ \varsigma\ \varphi</math>

blackboard bold \mathbb{N}\ \mathbb{Z}\ \mathbb{Q}\ \mathbb{R}\ \mathbb{C} <math>\mathbb{N}\ \mathbb{Z}\ \mathbb{Q}\ \mathbb{R}\ \mathbb{C}</math>
boldface (vectors) \mathbf{x}\cdot\mathbf{y} = 0 <math>\mathbf{x}\cdot\mathbf{y} = 0</math>
boldface (greek) \boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma} <math>\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}</math>
italics \mathit{ABCDE abcde 1234} <math>\mathit{ABCDE abcde 1234}\,\!</math>
Roman typeface \mathrm{ABCDE abcde 1234} <math>\mathrm{ABCDE abcde 1234}\,\!</math>
Fraktur typeface \mathfrak{ABCDE abcde 1234} <math>\mathfrak{ABCDE abcde 1234}</math>
Calligraphy/Script \mathcal{ABCDE abcde 1234} <math>\mathcal{ABCDE abcde 1234}</math>
Hebrew \aleph \beth \gimel \daleth <math>\aleph\ \beth\ \gimel\ \daleth</math>
non-italicised characters \mbox{abc} <math>\mbox{abc}</math> <math>\mbox{abc} \,\!</math>
mixed italics (bad) \mbox{if} n \mbox{is even} <math>\mbox{if} n \mbox{is even}</math> <math>\mbox{if} n \mbox{is even} \,\!</math>
mixed italics (good) \mbox{if }n\mbox{ is even} <math>\mbox{if }n\mbox{ is even}</math> <math>\mbox{if }n\mbox{ is even} \,\!</math>

[breyta] Parenthesizing big expressions, brackets, bars

Feature Syntax How it looks rendered
Not good ( \frac{1}{2} ) <math>( \frac{1}{2} )</math>
Better \left ( \frac{1}{2} \right ) <math>\left ( \frac{1}{2} \right )</math>

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

Feature Syntax How it looks rendered
Parentheses \left ( \frac{a}{b} \right ) <math>\left ( \frac{a}{b} \right )</math>
Brackets \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack <math>\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack</math>
Braces \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace <math>\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace</math>
Angle brackets \left \langle \frac{a}{b} \right \rangle <math>\left \langle \frac{a}{b} \right \rangle</math>
Bars and double bars \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \| <math>\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|</math>
Floor and ceiling functions: \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil <math>\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil</math>
Slashes and backslashes \left / \frac{a}{b} \right \backslash <math>\left / \frac{a}{b} \right \backslash</math>
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 <math>\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow</math>

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

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

<math>\left [ 0,1 \right )</math>
<math>\left \langle \psi \right |</math>

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

<math>\big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]</math>

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

<math>\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle</math>

\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big| <math>\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big|</math>
\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil

<math>\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil</math>

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

<math>\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow</math>

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

[breyta] Align with normal text flow

Due to the default css 

img.tex { vertical-align: middle; }

an inline expression like <math>\int_{-N}^{N} e^x\, dx</math> 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.

[breyta] Forced PNG rendering

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


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.-->

[breyta] Examples

--Freysteinn 20:41, 14. október 2005 (GMT) Þessi listi hér fyrir neðan er mjög klunnalegur, og ætti að vera sett í tvískipta töflu. Við ættum líka að vera með sýnidæmi sem eru betur flokkuð.

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

<math>x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

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

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

<math>4-2x = 9-3x \!</math>

<math>-2x+3x = 9-4 \!</math>

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

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

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

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

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

<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>

<math>\int_0^\infty x^\alpha \sin(x)\,dx = 2^\alpha \sqrt{\pi}\, \frac{\Gamma(\frac{\alpha}{2}+1)}{\Gamma(\frac{1}{2}-\frac{\alpha}{2})}\,</math>

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

<math>f(x) = {a_0\over 2} + \sum_{n=1}^\infty a_n\cos({2n\pi x \over T}) + b_n\sin({2n\pi x\over T})\,</math>

<math>f(x) = \begin{cases}1 & -1 \le x < 0\\ 

\frac{1}{2} & x = 0\\x&0<x\le 1\end{cases}</math>

<math>\Gamma(z) = \int_0^\infty e^{-t} t^{z-1} \,dt\,</math>

<math>J_p(z) = \sum_{k=0}^\infty \frac{(-1)^k\left(\frac{z}{2}\right)^{2k+p}}{k!\Gamma(k+p+1)}\,</math>

<math>{}_pF_q(a_1,...,a_p;c_1,...,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>

<math>\Gamma(n+1) = n \Gamma(n), n>0\,</math>

<math>\int_0^1 \frac{1}{\sqrt{-lnx}} dx\,</math>

<math>\int_0^\infty e^{-st}t^{x-1}\,dt,\,\,\,s>0\,</math>

<math>B(u) = \sum_{k=0}^N {P_k}{N! \over k!(N - k)!}{u^k}(1 - u)^{N-k}\,</math>

<math>u(x,y) = \frac{1}{\sqrt{2\pi}}\int_0^\infty f(\xi)\left[g(|x+\xi|,y)+g(|x-\xi|,y)\right]\,d\xi\,</math>

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