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2023-05-18T15:07:48Z

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{{Lua|Module:Infobox|Module:InfoboxImage|Module:Check for unknown parameters}}

{{Generic template demo |_display=italics |name |image={{{image}}} |parity |domain |codomain |range |period |zero |plusinf |minusinf |max |min |vr1 |f1 |vr2 |f2 |vr3=[...] |f3=[...] |vr5 |f5 |asymptote |root |critical |inflection |fixed |notes}}

== Blank syntax ==
<syntaxhighlight lang="wikitext">
{{Infobox mathematical function
| name =
| image= |imagesize=  |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 =
}}
</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 (mathematics)|fixed point]](s)
{{clear right}}

== Example ==

The code below produces the box opposite:
{{Infobox mathematical function
| name = Sine
| image = Sine one period.svg

|general_definition = <math>\sin(\alpha) = \frac {\textrm{opposite}} {\textrm{hypotenuse}}</math>

| parity=odd |domain=(−{{lower|0.2em|{{resize|130%|∞}}}}, +{{lower|0.2em|{{resize|130%|∞}}}}) {{smallsup|a}} |range=[−1, 1] {{smallsup|a}} |period=2{{pi}}
| zero=0 |plusinf= |minusinf=
|max=(2''k''{{pi}} + {{sfrac|{{pi}}|2}}, 1){{smallsup|b}} |min=(2''k''{{pi}} − {{sfrac|{{pi}}|2}}, −1)
| vr1= |f1=  |vr5= |f5=
| asymptote= |root=''k''{{pi}} |critical=''k''{{pi}} + {{sfrac|{{pi}}|2}} |inflection=''k''{{pi}} |fixed=0
| notes = {{ublist |{{sup|a}} For [[Real number|real]] numbers. |{{sup|b}} Variable ''k'' is an [[integer]].}}

|fields_of_application= [[Trigonometry]], [[Integral transform]], etc.
|date=[[Gupta period]]
|motivation_of_creation=[[Indian astronomy]]

|reciprocal = [[Cosecant]]
|inverse = [[Arcsine]]
|derivative = <math>f'(x) = \cos(x) </math>
|antiderivative = <math>\int f(x)\,dx = -\cos(x) + C </math>
|generalized_continued_fraction = <math>
\cfrac{x}{1 + \cfrac{x^2}{2\cdot3-x^2 +
\cfrac{2\cdot3 x^2}{4\cdot5-x^2 +
\cfrac{4\cdot5 x^2}{6\cdot7-x^2 + \ddots}}}}.
</math>
|taylor_series= <math>
\begin{align}
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{align}
</math>

|other_related= cos, tan, csc, sec, cot
}}

{{Infobox mathematical function
| name = Gamma
| image = Gamma plot.svg
| caption = The gamma function along part of the real axis

|general_definition = <math> \Gamma(z) = \int_0^\infty x^{z-1} e^{-x}\,dx \ </math>,<math>\qquad \Re(z) > 0\ </math>
| deriver = [[Daniel Bernoulli]]
|motivation_of_creation = [[Interpolation]] for factorial function
|extends = [[Factorial function]]
|date =1720s
|fields_of_application = [[Probability]], [[statistics]], [[combinatorics]]
|main_applications = probability-distribution functions

|domain={{math|<math>\mathbb{C}</math> - ℤ0-}}
|range=<math>\mathbb{C} \setminus \{0\} </math>

|parity=Not even and not odd
|period=No
|analytic = Yes
|meromorphic = Yes
|holomorphic = Yes except at ℤ0-
|plusinf= |minusinf=
|max= No |min= No
| asymptote=
|root= No
| notes =
| vr1={{math|ℤ+}} |f1= <math>(n-1)!</math>
|vr2={{math|ℤ0-}} |f2=Not defined
|fixed=<math>\supseteq</math> 1
|critical=<math>\supseteq</math> ℤ0-
|inflection=<math>\supseteq</math> ℤ0-
| poles = <math>\supseteq</math> ℤ0-

| corresponding_transform = [[Mellin transform]]
| corresponding_transform_formula =<math> \Gamma(z) = \{ \mathcal M e^{-x} \} (z).</math>
}}

<syntaxhighlight lang="wikitext">
{{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]].
}}
</syntaxhighlight>
{{clear right}}

== Tracking category ==
* {{clc|Pages using infobox mathematical function with unknown parameters}}

== See also ==
{{Math templates|BTN}}

<includeonly>{{basepage subpage|
[[Category:Mathematics infobox templates]]
[[Category:Statistics templates]]
[[Category:Templates that add a tracking category]]
}}</includeonly>

Template:Infobox mathematical function/doc - Revision history

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