Template:Infobox mathematical function/doc
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icon This is a documentation subpage for Template:Infobox mathematical function.
It may contain usage information, categories and other content that is not part of the original template page.
It may contain usage information, categories and other content that is not part of the original template page.
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
[edit ]{{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
[edit ]- 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
[edit ]The code below produces the box opposite:
| Sine | |
|---|---|
| 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),円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 }}}}}}}}.} |
| Gamma | |
|---|---|
| The gamma function along part of the real axis | |
| General information | |
| General definition | {\displaystyle \Gamma (z)=\int _{0}^{\infty }x^{z-1}e^{-x},円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} } - Z0- |
| Image | {\displaystyle \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+ | {\displaystyle (n-1)!} |
| Value at Z0- | Not defined |
| Specific features | |
| Root | No |
| Critical point | {\displaystyle \supseteq } Z0- |
| Inflection point | {\displaystyle \supseteq } Z0- |
| Fixed point | {\displaystyle \supseteq } 1 |
| Poles | {\displaystyle \supseteq } Z0- |
| 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+1⁄2)π,1) |min=((2k-1⁄2)π,-1) | asymptote= |root=kπ |critical=kπ-π/2 |inflection=kπ |fixed=0 | notes = Variable k is an [[integer]]. }}
Tracking category
[edit ]See also
[edit ]