Template:Infobox mathematical function

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name
[[File:{{{image}}}\|frameless]]
Domain, codomain and image
Domain	domain
Codomain	codomain
Image	range
Basic features
Parity	parity
Period	period
Specific values
At zero	zero
Value at +∞	plusinf
Value at −∞	minusinf
Maxima	max
Minima	min
Value at vr1	f1
Value at vr2	f2
Value at [...]	[...]
Value at vr5	f5
Specific features
Asymptote	asymptote
Root	root
Critical point	critical
Inflection point	inflection
Fixed point	fixed
notes

Blank syntax

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{{Infobox mathematical function
| name = 
| image= |imagesize= <!--(default 220px)--> |imagealt=
| parity= |domain= |codomain= |range= |period=
| zero= |plusinf= |minusinf= |max= |min=
| vr1= |f1= |vr2= |f2= |vr3= |f3= |vr4= |f4= |vr5= |f5=
| asymptote= |root= |critical= |inflection= |fixed=
| notes = 
}}

Parameters

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Pairs VR1-f1, f1-VR2, etc. are used for labeling specific value functions. Suppose a function at the point e has a value of 2e and that this point is because of something specific. In this case you should put that as VR1 = eand f1 = 2e. For the next point is used a couple of VR2-f2, etc. If you run out of points (five currently available), ask for more.
Variables heading1, heading2, heading3 define whether some of the headlines basic properties, specific values, etc. be displayed. If you do not want a title to be displayed, simply delete the variable from the template. Set the value of the variable to 0 or anything will not prevent the display title.
Variables plusinf and minusinf indicate the value function at + ∞ and - ∞.
root is the x-intercept, critical is the critical point(s), inflection is inflection point(s)
fixed is fixed point(s)

Example

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The code below produces the box opposite:

Sine

General information
General definition	$\sin(\alpha )={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}$ {\displaystyle \sin(\alpha )={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}}
Motivation of invention	Indian astronomy
Date of solution	Gupta period
Fields of application	Trigonometry, Integral transform, etc.
Domain, codomain and image
Domain	(−∞, +∞) ^a
Image	[−1, 1] ^a
Basic features
Parity	odd
Period	2π
Specific values
At zero	0
Maxima	(2kπ + ⁠π/2⁠, 1)^b
Minima	(2kπ − ⁠π/2⁠, −1)
Specific features
Root	kπ
Critical point	kπ + ⁠π/2⁠
Inflection point	kπ
Fixed point	0
Related functions
Reciprocal	Cosecant
Inverse	Arcsine
Derivative	$f'(x)=\cos(x)$ {\displaystyle f'(x)=\cos(x)}
Antiderivative	$\int f(x),円dx=-\cos(x)+C$ {\displaystyle \int f(x),円dx=-\cos(x)+C}
Other Related	cos, tan, csc, sec, cot
Series definition
Taylor series	${\begin{aligned}x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \\[8pt]&=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}$ {\displaystyle {\begin{aligned}x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \\[8pt]&=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}}
Generalized continued fraction	${\cfrac {x}{1+{\cfrac {x^{2}}{2\cdot 3-x^{2}+{\cfrac {2\cdot 3x^{2}}{4\cdot 5-x^{2}+{\cfrac {4\cdot 5x^{2}}{6\cdot 7-x^{2}+\ddots }}}}}}}}.$ {\displaystyle {\cfrac {x}{1+{\cfrac {x^{2}}{2\cdot 3-x^{2}+{\cfrac {2\cdot 3x^{2}}{4\cdot 5-x^{2}+{\cfrac {4\cdot 5x^{2}}{6\cdot 7-x^{2}+\ddots }}}}}}}}.}
^a For real numbers. ^b Variable k is an integer.

Gamma
The gamma function along part of the real axis
General information
General definition	$\Gamma (z)=\int _{0}^{\infty }x^{z-1}e^{-x},円dx\$ {\displaystyle \Gamma (z)=\int _{0}^{\infty }x^{z-1}e^{-x},円dx\ }, $\qquad \Re (z)>0\$ {\displaystyle \qquad \Re (z)>0\ }
Deriver of General definition	Daniel Bernoulli
Motivation of invention	Interpolation for factorial function
Date of solution	1720s
Extends	Factorial function
Fields of application	Probability, statistics, combinatorics
Main applications	probability-distribution functions
Domain, codomain and image
Domain	$\mathbb {C}$ {\displaystyle \mathbb {C} } - Z^0-
Image	$\mathbb {C} \setminus \{0\}$ {\displaystyle \mathbb {C} \setminus \{0\}}
Basic features
Parity	Not even and not odd
Period	No
Analytic?	Yes
Meromorphic?	Yes
Holomorphic?	Yes except at Z^0-
Specific values
Maxima	No
Minima	No
Value at Z⁺	$(n-1)!$ {\displaystyle (n-1)!}
Value at Z^0-	Not defined
Specific features
Root	No
Critical point	$\supseteq$ {\displaystyle \supseteq } Z^0-
Inflection point	$\supseteq$ {\displaystyle \supseteq } Z^0-
Fixed point	$\supseteq$ {\displaystyle \supseteq } 1
Poles	$\supseteq$ {\displaystyle \supseteq } Z^0-
Transform
Corresponding transform	Mellin transform
Corresponding transform formula	$\Gamma (z)=\{{\mathcal {M}}e^{-x}\}(z).$ {\displaystyle \Gamma (z)=\{{\mathcal {M}}e^{-x}\}(z).}

{{Infobox mathematical function
| name = Sine
| image = Sinus.svg
| parity=odd |domain=(-∞,∞) |range=[-1,1] |period=2π
| zero=0 |plusinf= |minusinf= |max=((2k+1⁄2)π,1) |min=((2k-1⁄2)π,-1)
| asymptote= |root=kπ |critical=kπ-π/2 |inflection=kπ |fixed=0
| notes = Variable k is an [[integer]].
}}

Tracking category

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Category:Pages using infobox mathematical function with unknown parameters (0)

Conversions
convert many units (see: list) cvt abbreviated {{convert }} convinfobox {{convert }} for infoboxes bbl to t barrels of oil to tonnes long ton long hundredweights, quarters and pounds to kilograms; long tons and hundredweights to pounds and metric tons miles-chains miles and chains to kilometres linking "chains"		decdeg degrees, minutes, and seconds to decimal degrees deg2dms decimal degrees to degrees, minutes, and seconds deg2hms decimal degrees to hour angle (in hours, minutes, and seconds) hms2deg hour angle (in hours, minutes, and seconds) to decimal degrees inflation calculate inflation of Consumer Price Index-related prices pop density population density in an area track gauge railway track gauges

Notation and formatting
bigmath bigger font to match TeX `\displaystyle` (standalone formulas only) bra-ket braket bra ket bra–ket notation ceil, floor calculations :mw:Help:#expr; formatting indicators ⌈3.14⌉, ⌊3.14⌋ (no calculation performed) fraction slant fractions 3⁄5 (not for maths/science articles; use standing or upright fractions `{{sfrac}}` instead) intmath integral symbols langle rangle angbr angular brackets ldelim rdelim multiline delimiters (2–5 lines inclusive) abs absolute values (paired vertical lines) math short text-based formulas mathcal [mathematical] calligraphic font; alternative to LaTeX `\mathcal{...}`		mvar individual italicized maths variables in normal text overline underline a line set above/below a sequence of characters overarc an arc set above a sequence of characters overset underset arbitrary characters/diacritics set above/below one another pars parentheses that can be resized (∑) sfrac "standing" or upright fractions ⁠3/5⁠ (use in maths/science articles instead of`{{fraction}}`) sub sup su subscripts and superscripts tmath Wrap TeX in <math> tags tombstone symbol indicating the end of a proof val measurement values, uncertainties and units vec various overarrows, underarrows, etc.

Boxes Tags Notices
Boxes Tags arithmetic operations calculus Infobox mathematical function functions metricate undue precision units attention

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Blank syntax

Parameters

Example

Tracking category

See also