Template:Infobox mathematical function/doc

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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=(2kππ/2, −1) | vr1= |f1= |vr5= |f5= | asymptote= |root=kπ |critical=kπ + π/2 |inflection=kπ |fixed=0

| notes =

|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 definitionDaniel Bernoulli
Motivation of inventionInterpolation for factorial function
Date of solution1720s
ExtendsFactorial function
Fields of applicationProbability, statistics, combinatorics
Main applicationsprobability-distribution functions
Domain, Codomain and Image
Domain<math>\mathbb{C}</math> - ℤ0-
Image<math>\mathbb{C} \setminus \{0\} </math>
Basic features
ParityNot even and not odd
PeriodNo
Analytic?Yes
Meromorphic?Yes
Holomorphic?Yes except at ℤ0-
Specific values
MaximaNo
MinimaNo
Value at +<math>(n-1)!</math>
Value at 0-Not defined
Specific features
RootNo
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 transformMellin 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

See also

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