This is a documentation subpage for Template:Infobox mathematical function. It may contain usage information, categories and other content that is not part of the original template page.

This template uses Lua: Module:Infobox (sandbox) Module:InfoboxImage Module:Check for unknown parameters

((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 = 
))

• 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)

The code below produces the box opposite:

Sine
General information
General definition	${\displaystyle \sin(\alpha )={\frac {\textrm {opposite)){\textrm {hypotenuse))))$
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	${\displaystyle f'(x)=\cos(x)}$
Antiderivative	${\displaystyle \int f(x)\,dx=-\cos(x)+C}$
Other Related	cos, tan, csc, sec, cot
Series definition
Taylor series	${\displaystyle {\begin{aligned}x-{\frac {x^{3)){3!))+{\frac {x^{5)){5!))-{\frac {x^{7)){7!))+\cdots \\[8pt]&=\sum _{n=0}^{\infty }{\frac {(-1)^{n)){(2n+1)!))x^{2n+1}\\[8pt]\end{aligned))}$
Generalized continued fraction	${\displaystyle {\cfrac {x}{1+{\cfrac {x^{2)){2\cdot 3-x^{2}+{\cfrac {2\cdot 3x^{2)){4\cdot 5-x^{2}+{\cfrac {4\cdot 5x^{2)){6\cdot 7-x^{2}+\ddots )))))))).}$
a For real numbers. b Variable k is an integer.

Gamma
The gamma function along part of the real axis
General information
General definition	${\displaystyle \Gamma (z)=\int _{0}^{\infty }x^{z-1}e^{-x}\,dx\ }$,${\displaystyle \qquad \Re (z)>0\ }$
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	${\displaystyle \mathbb {C} }$ - ℤ0-
Image	${\displaystyle \mathbb {C} \setminus \{0\))$
Basic features
Parity	Not even and not odd
Period	No
Analytic?	Yes
Meromorphic?	Yes
Holomorphic?	Yes except at ℤ0-
Specific values
Maxima	No
Minima	No
Value at ℤ+	${\displaystyle (n-1)!}$
Value at ℤ0-	Not defined
Specific features
Root	No
Critical point	${\displaystyle \supseteq }$ ℤ0-
Inflection point	${\displaystyle \supseteq }$ ℤ0-
Fixed point	${\displaystyle \supseteq }$ 1
Poles	${\displaystyle \supseteq }$ ℤ0-
Transform
Corresponding transform	Mellin transform
Corresponding transform formula	${\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+½)π,1) |min=((2k-½)π,-1)
| asymptote= |root=kπ |critical=kπ-π/2 |inflection=kπ |fixed=0
| notes = Variable k is an [[integer]].
))

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

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