Template:Infobox mathematical function

Gamma
Gamma
	The gamma function along part of the real axis
General information
General definition	,
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	- ℤ0-
Image
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+
Value at ℤ0-	Not defined
Specific features
Root	No
Critical point	ℤ0-
Inflection point	ℤ0-
Fixed point	1
Poles	ℤ0-
Transform
Corresponding transform	Mellin transform
Corresponding transform formula

Sine
Sine
General information
General definition
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
Antiderivative
Other Related	cos, tan, csc, sec, cot
Series definition
Taylor series
Generalized continued fraction
	a For real numbers.; b Variable k is an integer.;

*name*
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

Template documentation

Blank syntax

{{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

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

The code below produces the box opposite:

{{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]].}}

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Template:Infobox mathematical function

Contents

Blank syntax

Parameters

Example

Tracking category

See also

Sine

General information
General definition	$\sin(\alpha )={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}$
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	2 $π$
Specific values
At zero	0
Maxima	(2k $π$ + $π$ /2, 1)^b
Minima	(2k $π$ − $π$ /2, −1)
Specific features
Root	k $π$
Critical point	k $π$ + $π$ /2
Inflection point	k $π$
Fixed point	0
Related functions
Reciprocal	Cosecant
Inverse	Arcsine
Derivative	$f'(x)=\cos(x)$
Antiderivative	$\int f(x)\,dx=-\cos(x)+C$
Other Related	cos, tan, csc, sec, cot
Series definition
Taylor series	${\begin{aligned}x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \\[8pt]&=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}$
Generalized continued fraction	${\cfrac {x}{1+{\cfrac {x^{2}}{2\cdot 3-x^{2}+{\cfrac {2\cdot 3x^{2}}{4\cdot 5-x^{2}+{\cfrac {4\cdot 5x^{2}}{6\cdot 7-x^{2}+\ddots }}}}}}}}.$
^a For real numbers. ^b Variable k is an integer.