Template:Infobox mathematical function

File:Test Template Info-Icon - Version (2).svg Template documentation[view] [edit] [history] [purge]

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

{{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:

Sine
File:Sine one period.svg
General information
General definition	$\sin (\alpha )=\frac{\text{<mrow data-mjx-texclass="ORD">opposite</mrow>}}{\text{<mrow data-mjx-texclass="ORD">hypotenuse</mrow>}}$
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	$f^{\prime }(x)=\cos (x)$
Antiderivative	$\int f(x)dx=-\cos (x)+C$
Other Related	cos, tan, csc, sec, cot
Series definition
Taylor series	$\begin{array}{r}x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\cdots \\ & =\sum _{n=0}^{\mathrm{\infty }}\frac{(-1{)}^n}{(2n+1)!}{x}^{2n+1}\\ \end{array}$
Generalized continued fraction	$\frac{x}{1+\frac{x^2}{2\cdot 3-x^2+\frac{2\cdot 3x^2}{4\cdot 5-x^2+\frac{4\cdot 5x^2}{6\cdot 7-x^2+\ddots }}}}.$
a For real numbers. b Variable k is an integer.

Gamma
File:Gamma plot.svg The gamma function along part of the real axis
General information
General definition	$\mathrm{\Gamma }(z)=\underset{0}{\overset{\mathrm{\infty }}{\int }}{x}^{z-1}{e}^{-x}dx$,$\mathrm{\Re }(z)>0$
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	$\mathbb{ℂ}$ - ℤ0-
Image	$\mathbb{ℂ}\setminus \{0\}$
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+	$(n-1)!$
Value at ℤ0-	Not defined
Specific features
Root	No
Critical point	$\supseteq$ ℤ0-
Inflection point	$\supseteq$ ℤ0-
Fixed point	$\supseteq$ 1
Poles	$\supseteq$ ℤ0-
Transform
Corresponding transform	Mellin transform
Corresponding transform formula	$\mathrm{\Gamma }(z)=\{{ℳ}{e}^{-x}\}(z).$

{{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]].
}}

Tracking category

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

See also

The above documentation is transcluded from Template:Infobox mathematical function/doc. (edit | history)
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