## Math Notation Help

This glossary will help you build complex mathematical equations using the Tex markup language. This will involve using @@ or $$before and after the expression to display the desired results. Browse the glossary using this index Special | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | ALL Page: 1 2 3 4 5 6 7 8 9 10 ... 12 (Next) ALL ### \ #### \_ (where _ is blank) • Ordinary whitespace to be used after a dot not denoting the end of a sentence • After commands without parameters use \~ (tilde) instead in order to avoid browser specific problems  Keyword(s): math spaces, whitespace, blank space #### \, • \, inserts the smallest predefined space in a formula • Equivalent: \hspace{2} • Ex.:$$a\,b$gives$a\,b$
• Ex.: a~\hspace{2}~b$
• $gives also $a~\hspace{2}~b$  Keyword(s): math spaces #### \; • \; (backslash semicolon) inserts the third smallest predefined space in a formula • Equivalent: \hspace{6} • Ex.: $$a\;b$gives$a\;b$ • Ex.: a~\hspace{6}~b$ • gives also $a~\hspace{6}~b$  Keyword(s): math spaces #### \: • \: inserts the second smallest predefined space in a formula • Equivalent: \hspace{4} • Ex.:$$a\:b$gives$a\:b$ • Ex.: a~\hspace{4}~b$ •$ gives also $a~\hspace{4}~b$
 Keyword(s): math spaces

#### \/ (backslash slash)

• \/ (backslash slash) avoids ligatures

f(x)=3a+x$$#### contour integral • General syntax for symbols with a kind of lower and upper limits: \symbolname_{lowerexpression}^{upperexpression} • In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix. • Syntax for the contour integral symbol:$$\bigoint_{0}^{\infty}gives

\bigoint_{0}^{\infty}

and

\oint_{0}^{\infty}

$gives $\oint_{0}^{\infty}$ • Use font size commands for a nicer picture: $$\LARGE\bigoint_{\small0}^{\small\infty}gives \LARGE\bigoint_{\small0}^{\small\infty} and \large\oint_{\small0}^{\small\infty} gives $\large\oint_{\small0}^{\small\infty}$ #### coproduct • General syntax for symbols with a kind of lower and upper limits: \symbolname_{lowerexpression}^{upperexpression} • In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix. • Note: mimeTeX seems currently only to support the \bigcoprod command. • Syntax for coproduct symbol:$$\bigcoprod_{i=k}^{n}gives \bigcoprod_{i=k}^{n} • Use font size commands for a nicer picture: \LARGE\bigcoprod_{\small{i=k}}^{\small~n}$   gives

$\LARGE\bigcoprod_{\small{i=k}}^{\small~n}$

 Keyword(s): coprod

### D

#### delimiters (overview)

 Delimiters (parentheses, braces, brackets. ...) Command Example Result \left(... \right) $$2\left(a+b\right)2~\left(a+b\right)$$ \left[... \right] $$\left[a^2+b^2~\right]\left[a^2+b^2~\right]$$ \left{... \right} $$\left{x^2, x^3, x^4,... \right}\left{x^2, x^3, x^4,... \right}$$ \left\langle... \right\rangle $$\left\langle a,b~\right\rangle\left\langle a,b~\right\rangle$$ \left| ... \right| $$\det\left|\array{a&b\\c&d}\right| \det\left|\array{a&b\\c&d}\right|$$ \left\| ... \right\| $$\left\|f~\right\|\left\|f~\right\|$$ \left{ ... \right.(note the dot!) $$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.(\rm switches to roman style)f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$ \left.{ ... \right\}(note the dot!) $$\left.{{\rm~term1\atop\rm~term2}\right}=y\left.{{\rm~term1\atop \rm~term2}\right}=y$$

Note: The delimiters are automatically sizes.

#### delta

$$\delta$is$\delta$$
 Keyword(s): delta

#### Delta (upper case greek letter)

$$\Delta$gives$\Delta$$

#### delta (lower case greek letter)

$$\delta$gives$\delta$$
 Keyword(s): delta

#### div (division)

$$x\div~y$gives$x\div~y$$

#### division

 Keyword(s): division/

#### double vertical line (norm symbol)

• Syntax: \left\|...\right\|
• Exp.: $$\left\|af\right\| = \left|a\right|\left\|f\right\|gives \left\|af\right\| = \left|a\right|\left\|f\right\|$$

 Keyword(s): norm

### E

#### epsilon (lower case greek letter)

$$\epsilon$gives$\epsilon$$

#### equals

 Keyword(s): =equals

#### escaping the TeX filter

• With two triple $'s embracing an expression you can make the filter to escape and the code itself is shown (with two embracing double$'s).
• Ex.: $$a^2$$$produces $$a^2$$$, i.e. prevents the filter to render it as a formula gif.
 Keyword(s): escape; suppress filter; prevent from filtering

#### eta (lower case greek letter)

$$\eta$gives$\eta$$

### F

#### formula box

$$\fbox{x=\frac{1}{2}}gives \fbox{x=\frac{1}{2}}$$

 Keyword(s): fbox

#### fraction

• Syntax: \frac{numerator}{denominator}
• Use font sizing commands for specific sizing if you don't want the predefined one to be taken.
• Ex. (with predefined sizing): $$f(x,y)=\frac{2a}{x+y}gives f(x,y)=\frac{2a}{x+y}$$

• Ex. (with specific sizing): $$f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}gives f(x,y)=\frac{\fs{2}2a}{\fs{2}x+y}$$

• You may nest fractions as much as you want.
• Ex. (nested fractions): $$\frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}gives \frac{\frac{a}{x-y}+\frac{b}{x+y}}{1+\frac{a-b}{a+b}}$$

### G

#### gamma (lower case greek letter)

$$\gamma$gives$\gamma$$

#### Gamma (upper case greek letter)

$$\Gamma$gives$\Gamma$$

#### greater than

$$x>ygives x>y$$

 Keyword(s): >greater than

$$x\ge~y$or x\geq~y$ gives $x\ge~y$  Keyword(s): >= #### greek letters (overview) Simply write \greekletter for lower case and \Greekletter for upper case. Here's a list of all known greek letters (Note: not all upper case greek letters are known): Lower Case Greek Letters:  Command Filter Expression Result \alpha$$\alpha\alpha$$\beta$$\beta\beta$$\gamma$$\gamma\gamma$$\delta$$\delta\delta$$\epsilon$$\epsilon\epsilon$$\varepsilon$$\varepsilon\varepsilon$$\zeta$$\zeta\zeta$$\eta$$\eta\eta$$\theta$$\theta\theta$$\vartheta$$\vartheta\vartheta$$\iota$$\iota\iota$$\kappa$$\kappa\kappa$$\lambda$$\lambda\lambda$$\mu$$\mu\mu$$\nu$$\nu\nu$$\xi$$\xi\xi$$o (!)$$oo$$\pi$$\pi\pi$$\varpi$$\varpi\varpi$$\rho$$\rho\rho$$\varrho$$\varrho\varrho$$\sigma$$\sigma\sigma$$\varsigma$$\varsima\varsigma$$\tau$$\tau\tau$$\upsilon$$\upsilon\upsilon$$\phi$$\phi\phi$$\varphi$$\varphi\varphi$$\chi$$\chi\chi$$\psi$$\psi\psi$$\omega$$\omega\omega$$Upper Case Greek Letters:  Command Filter Expression Result \Gamma$$\Gamma\Gamma$$\Delta$$\Delta\Delta$$\Theta$$\Theta\Theta$$\Lambda$$\Lambda\Lambda$$\Xi$$\Xi\Xi$$\Pi$$\Pi\Pi$$\Sigma$$\Sigma\Sigma$$\Upsilon$$\Upsilon\Upsilon$$\Phi$$\Phi\Phi$$\Psi$$\Psi\Psi$$\Omega$$\Omega\Omega$$### I #### infinity$$\infty$gives$\infty$$ Keyword(s): infinity #### integral • General syntax for symbols with a kind of lower and upper limits: \symbolname_{lowerexpression}^{upperexpression} • In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix. • Syntax for integral symbol:$$\bigint_{0}^{\infty}gives

\bigint_{0}^{\infty}

and

\int_{0}^{\infty}

$gives $\int_{0}^{\infty}$ • Use font size commands for a nicer picture: $$\LARGE\bigint_{\small0}^{\small\infty}gives \LARGE\bigint_{\small0}^{\small\infty} and \large\int_{\small0}^{\small\infty} gives $\large\int_{\small0}^{\small\infty}$  Keyword(s): int #### iota (lower case greek letter)$$\iota$gives$\iota$$### K #### kappa$$\kappa$gives$\kappa$$### L #### lambda (lower case greek letter)$$\lambda$gives$\lambda$$#### Lambda (upper case greek letter)$$\Lambda$gives$\Lambda$$#### Learning Formula $\frac{success}{problem}=~\unitlength{.6}~\picture(100){~~(50,50){\circle(99)}~ ~(20,55;50,0;2){+1\hat\bullet}~~(50,40){\bullet}~~(50,35){\circle(50,25;34)}~ ~(50,35){\circle(50,45;34)}}$  Keyword(s): learning formula #### left only brace • Syntax: \left{...\right. (note the dot at the end!) • Ex.:$$f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.gives f(x)=\left{{x^2, \rm~if x>-1\atop~0, \rm~else}\right.$$(\rm~something switches to roman style) #### less than$$<gives <$$ Keyword(s): less than< #### less than or equal$$x\le~y$or x\leq~y$$ gives

$x\le~y$

 Keyword(s): <=

### M

#### math spaces

List of predefined spaces:

\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)Note in the example above that "lcr" has the effect that column 1 is left aligned, column 2 centered and colums 3 right aligned.  Keyword(s): matrix, array #### minus-$is$-$$ Keyword(s): -minus #### minus plus$$\mp~a$gives$\mp~a$$#### mu (lower case greek letter)$$\mu$gives$\mu$$#### multiplication$$x*y=z$is$x*y=z$$ Keyword(s): multiplicationmultiply #### multiplication (with cdot)$$a\cdot~b$gives$a\cdot~b$$ Keyword(s): cdot ### N #### not equal$$x\neq~ygives

x\neq~y$$note: \neg produces the logical negation, i.e.$$\neg~Agives

2a\left(b+c\right)$$#### phi (lower case greek letter)$$\phi$gives$\phi$$#### Phi (upper case greek letter)$$\Phi$gives$\Phi$$#### pi$$x=\pi r^2$is$x=\pi r^2$$ Keyword(s): pi #### pi (lower case greek letter)$$\pi$gives$\pi$$#### Pi (upper case greek letter)$$\Pi$gives$\Pi$$#### plus$$+$is$+$$ Keyword(s): +plus #### plus minus$$a\pm~b$gives$a\pm~b$$#### product • General syntax for symbols with a kind of lower and upper limits: \symbolname_{lowerexpression}^{upperexpression} • In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix. • Syntax for product symbol:$$\bigprod_{i=k}^{n}gives

\bigprod_{i=k}^{n}

and

\prod_{i=k}^{n}

$gives $\prod_{i=k}^{n}$ • Use font size commands for a nicer picture: $$\LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}}gives \LARGE\bigprod_{\tiny{i=k}}^{\tiny{n}} and \large\prod_{\small{i=k}}^{\small{n}} gives $\large\prod_{\small{i=k}}^{\small{n}}$ #### psi (lower case greek letter)$$\psi$gives$\psi$$#### Psi (upper case greek letter)$$\Psi$gives$\Psi$$### R #### relativity $E=mc^2$  Keyword(s): relativity #### rho (lower case greek letter)$$\rho$gives$\rho$$#### right only brace • Syntax: \left.{...\right} (note the dot!) • Ex.:$$\left.{{\rm~term1\atop\rm~term2}\right}=ygives \left.{{\rm~term1\atop\rm~term2}\right}=y$$(\rm~something switches to roman style) #### root • Syntax: \sqrt[n]{arg} or simply \sqrt{arg} for \sqrt{arg} • Ex.:$$\sqrt{8}gives \sqrt{8}$$• Ex.:$$\sqrt{-1}gives \sqrt{-1}$$• Nesting of roots (and combining with fractions, ...etc.) are possible. • Ex.:$$\sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}gives \sqrt[n]{\frac{x^n-y^n}{1+u^{2n}}}$$• Ex.:$$\sqrt{-q+\sqrt{q^2+p^3}}gives \sqrt{-q+\sqrt{q^2+p^3}}$$ Keyword(s): square root ### S #### s.u.m$$\sum_{n+2}^x$is$\sum_{n+2}^x$$ Keyword(s): sum #### sigma (lower case greek letter)$$\sigma$gives$\sigma$$#### Sigma (upper case greek letter)$$\Sigma$gives$\Sigma$$#### smiley$$~\unitlength{.6}~\picture(100){~~(50,50){\circle(99)}~ ~(20,55;50,0;2){+1$\hat\bullet}~~(50,40){\bullet}~~(50,35){\circle(50,25;34)}~ ~(50,35){\circle(50,45;34)}}$is$~\unitlength{.6}~\picture(100){~~(50,50){\circle(99)}~ ~(20,55;50,0;2){+1$\hat\bullet}~~(50,40){\bullet}~~(50,35){\circle(50,25;34)}~ ~(50,35){\circle(50,45;34)}}$$ Keyword(s): smiley #### square bracket • Synatx: \left[...\right] • Ex.:$$\left[a,b\right]$gives$\left[a,b\right]$$#### square root •$$\sqrt{a}$or \sqrt~a$$ gives $\sqrt~a$
• Use braces for terms with more than one character: $$\sqrt{x+y}gives \sqrt{x+y}$$

#### subscript

• The command character "_" triggers subscription of the following expression(s).
• For more than one subscripted character put them in braces {...}.
• Use font sizing commands for appropriate sizing.
• Ex.:$$x_1gives x_1$$

• Ex.:$$a_{m+2n}gives a_{m+2n}$$

• Ex. (with specific sizing):  $$x_{\small1}=a_{\small{m+2n}}gives x_{\small1}=a_{\small{m+2n}}$$

• Combine subscripting with superscripting (command character "^").
Syntax: Expr_{subExpr}^{supExpr}.
• Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}gives A_{\small{i,j,k}}^{\small{-n+2}}$$

#### sum (summation)

• General syntax for symbols with a kind of lower and upper limits:

\symbolname_{lowerexpression}^{upperexpression}

• In general, there are two ways how these lower and upper expressions can be placed: centered below and above the symbol or in a subscript / superscript manner. In the first case the symbol name is preceded by the word "big", in the second there is no prefix.
• Syntax for summation symbol:

$$\bigsum_{i=k}^{n}gives \bigsum_{i=k}^{n} and \sum_{i=k}^{n}  gives $\sum_{i=k}^{n}$ • Use font size commands for a nicer picture:$$\LARGE\bigsum_{\small{i=1}}^{\small{n}}gives

\LARGE\bigsum_{\small{i=1}}^{\small{n}}

and

\large\sum_{\small{i=1}}^{\small{n}}

$gives $\large\sum_{\small{i=1}}^{\small{n}}$  Keyword(s): big sum #### superscript • The command character "^" triggers superscription of the following expression(s). • For more than one superscripted character put them in braces {...}. • Use font sizing commands for appropriate sizing. • Ex.: $$x^2gives x^2$$ • Ex.: $$a^{m+2n}gives a^{m+2n}$$ • Ex. (with specific sizing): $$x^{\small2}=a^{\small{m+2n}}gives x^{\small2}=a^{\small{m+2n}}$$ • Combine superscripting with subscripting (command character "_"). Syntax: Expr_{subExpr}^{supExpr}. • Ex.: $$A_{\small{i,j,k}}^{\small{-n+2}}gives A_{\small{i,j,k}}^{\small{-n+2}}$$ ### T #### tau (lower case greek letter) $$\tau$gives$\tau$$ #### TeX $TeX$ notation allows for the expression of ASCII characters to generate formatted graphics output  Keyword(s): TeX #### theta (lower case greek letter) $$\theta$gives$\theta$$ #### Theta (upper case greek letter) $$\Theta$gives$\Theta$$ #### times $$a\times~b$gives$a\times~b$$ #### triangle $$\triangle~abc$gives$\triangle~abc$$  Keyword(s): triangle #### triggering the TeX filter • Two double$'s embracing a valid math expression trigger the filter to generate and insert the formula gif.
• Ex.:  $$a^2$produces$a^2$$
 Keyword(s): trigger, TeX filter, start filter

### U

#### upsilon (lower case greek letter)

$$\upsilon$gives$\upsilon$$

#### Upsilon (upper case greek letter)

$$\Upsilon$gives$\Upsilon$$

### V

#### varepsilon (special lower case greek letter)

$$\varepsilon$gives$\varepsilon$$

#### variables

• Variables in formulas are rendered in italic roman font face, which is a widely used convention.
• Following this convention, constants are shown as non-italic.
• Exp.: $$f(x)=3a+xgives f(x)=3a+x$$

#### varphi (special lower case greek letter)

$$\varphi$gives$\varphi$$

#### varpi (special lower case greek letter)

$$\varpi$gives$\varpi$$

#### varrho (special lower case greek letter)

$$\varrho$gives$\varrho$$

#### varsigma (special lower greek letter)

$$\varsigma$gives$\varsigma$$

#### vartheta (special lower case greek letter)

$$\vartheta$gives$\vartheta$$

#### vertical line (absolute value, determinant, ...etc. symbol)

• Syntax: \left|...\right|
• Ex.: $$\left|b-a\right|$gives$\left|b-a\right|$ • Ex.: {\rm~det}\left|\begin{array}{cc}a&b\\c&d \end{array}\right|$ •  gives ${\rm~det}\left|\begin{array}{cc}a&b\\c&d \end{array}\right|$ ("\rm~something" renders "something" in roman style)  Keyword(s): absolute value symbol, determinant symbol ### X #### xi (lower case greek letter)$$\xi$gives$\xi$$#### Xi (upper case greek letter)$$\Xi$gives$\Xi$$### Z #### zeta (lower case greek letter)$$\zeta$gives$\zeta

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