Template:Infobox mathematical function

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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	<math>\sin(\alpha) = \frac {\textrm{opposite

{\textrm{hypotenuse}}</math>

| parity=odd |domain=(−∞, +∞) ^a |range=[−1, 1] ^a |period=2π | zero=0 |plusinf= |minusinf= |max=(2kπ + π/2, 1)^b |min=(2kπ − π/2, −1) | vr1= |f1= |vr5= |f5= | asymptote= |root=kπ |critical=kπ + π/2 |inflection=kπ |fixed=0

| notes =

• ^a For real numbers.
• ^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 }}

Gamma
File:Gamma plot.svg The gamma function along part of the real axis
General information
General definition	<math> \Gamma(z) = \int_0^\infty x^{z-1} e^{-x}\,dx \ </math>,<math>\qquad \Re(z) > 0\ </math>
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	<math>\mathbb{C}</math> - ℤ0-
Image	<math>\mathbb{C} \setminus \{0\} </math>
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+	<math>(n-1)!</math>
Value at ℤ0-	Not defined
Specific features
Root	No
Critical point	<math>\supseteq</math> ℤ0-
Inflection point	<math>\supseteq</math> ℤ0-
Fixed point	<math>\supseteq</math> 1
Poles	<math>\supseteq</math> ℤ0-
Transform
Corresponding transform	Mellin transform
Corresponding transform formula	<math> \Gamma(z) = \{ \mathcal M e^{-x} \} (z).</math>

{{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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