Voozh

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👁 Image
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This template uses Lua:

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
👁 Image
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
👁 Image 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} } - ℤ^0-
Image	👁 {\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⁺	👁 {\displaystyle (n-1)!}
Value at ℤ^0-	Not defined
Specific features
Root	No
Critical point	👁 {\displaystyle \supseteq } ℤ^0-
Inflection point	👁 {\displaystyle \supseteq } ℤ^0-
Fixed point	👁 {\displaystyle \supseteq } 1
Poles	👁 {\displaystyle \supseteq } ℤ^0-
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]].
}}

Tracking category

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

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

Boxes

URL: https://en.wikipedia.org/wiki/Template:Infobox_mathematical_function

⇱ Template:Infobox mathematical function - Wikipedia

Blank syntax

Parameters

Example

Tracking category

See also