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

<syntaxhighlight lang="wikitext">

Infobox mathematical function

</syntaxhighlight>

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
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	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	$f'(x)=\cos(x)$
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.

Gamma
The gamma function along part of the real axis
General information
General definition	$\Gamma (z)=\int _{0}^{\infty }x^{z-1}e^{-x}\,dx\$,$\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	$\mathbb {C}$ - 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	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \supseteq} 1
Poles	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \supseteq} ℤ0-
Transform
Corresponding transform	Mellin transform
Corresponding transform formula	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Gamma(z) = \{ \mathcal M e^{-x} \} (z).}

<syntaxhighlight lang="wikitext">

Sine
Domain, codomain and image
Domain	(-∞,∞)
Image	[-1,1]
Basic features
Parity	odd
Period	2π
Specific values
At zero	0
Maxima	((2k+½)π,1)
Minima	((2k-½)π,-1)
Specific features
Root	kπ
Critical point	kπ-π/2
Inflection point	kπ
Fixed point	0
Variable k is an integer.

</syntaxhighlight>

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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