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2023-05-21T06:57:18Z

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{{Documentation subpage}}
{{Uses TemplateStyles|Template:Infobox combinatorial classes/styles.css}}

=== Usage ===
The '''Template:infobox combinatorial classes''' generates a right-hand side infobox, based on the specified parameters. To use this template, copy the following code in your article and fill in as appropriate:

{{Parameter names example| name| notation| intro| parameters| nth_element| asymptotic| support| OGF | OGF radius | EGF | EGF radius | PGF | PGF radius | LS | LS radius | BS | BS radius | DGF | DGF radius_ | PSGF | PSGF radius}}

<syntaxhighlight lang="wikitext">
{{Infobox combinatorial classes
| name =
| notation =
| intro =
| parameters =
| nth_element =
| asymptotic =
| support =
| OGF =
| OGF radius =
| EGF =
| EGF radius =
| PGF =
| PGF radius =
| LS =
| LS radius =
| BS =
| BS radius =
| DGF =
| DGF radius =
| PSGF =
| PSGF radius =
}}
</syntaxhighlight>

==== Parameters ====
* '''name''' — Name at the top of the infobox; should be the name of the sequence, without the word sequence. (e.g. "Fibonnacci", "Factorials")
* '''notation''' — How the sequence (or its <math>n</math>-th element) is usually denoted. For example, <math>n!</math> for the sequence of factorials.
* '''parameters''' — parameters of the sequence family.
* '''support''' — Where the sequence is defined and non-zero. (e.g. it is the place to state that a sequence has only value at even position, or at prime positions.)
* '''nth element''' — The place to give the exact value of the <math>n</math>-th element of the sequence. (e.g. for fibonnaci number, it would be <math>\frac{1}{\sqrt5}\left(\left(\frac{1+\sqrt 5}{2}\right)^n+\left(\frac{1-\sqrt 5}{2}\right)^n\right)</math>)
* '''asymptotic''' — A function with the same domain than the sequence, which is asymptotically equivalent to it. (e.g. for fibonnaci number, it would be <math>\frac{1}{\sqrt5}\left(\left(\frac{1+\sqrt 5}{2}\right)^n\right)</math>)
* '''OGF''', '''EGF''', '''PGF''', '''LS''', '''BS''', '''DGF''', '''PSGF''' are defined as in the page [[Generating function]]
* '''OGF radius''', '''EGF radius''', '''PGF radius''', '''LS radius''', '''BS radius''', '''DGF radius''', '''PSGF radius''' the radius of the previously defined functions

==TemplateData==

{{TemplateData header|noheader=1}}
<templatedata>
{
"params": {
"box_width": {},
"name": {
"label": "Name",
"description": "Name at the top of the infobox; should be the name of the sequence, without the word sequence",
"example": "Fibonnacci"
},
"notation": {},
"intro": {},
"parameters": {},
"support": {
"description": "Where the sequence is defined and non-zero.",
"example": "The even numbers. The prime numbers"
},
"nth element": {},
"asymptotic": {
"description": "A function with the same domain than the sequence, which is asymptotically equivalent to it.",
"example": "<math>\\frac{1}{\\sqrt5}\\left(\\left(\\frac{1+\\sqrt 5}{2}\\right)^n\\right)</math> for Fibonnacci"
},
"OGF": {
"description": "The ordinary generating function of the sequence"
},
"radius_OGF": {
"label": "its radius",
"description": "radius of convergence of the OGF",
"example": "1",
"type": "number"
},
"EGF": {
"description": "The exponential generating function of the sequence"
},
"radius_EGF": {
"description": "the radius of convergence of the EGF"
},
"PGF": {
"description": "The poisson generating function of the sequence"
},
"radius_PGF": {
"description": "the radius of convergence of the PGF"
},
"LS": {
"description": "The Lambert series of the sequence"
},
"radius_LS": {
"description": "the radius of convergence of the LS"
},
"BS": {
"description": "The Bell series of the sequence"
},
"radius_BS": {
"description": "the radius of convergence of the BS"
},
"DGF": {
"description": "The Dirichlet series generating functions of the sequence"
},
"radius_DGF": {
"description": "the radius of convergence of the DGF"
},
"PSGF": {
"description": "The Polynomial Sequence Generating Function of the sequence"
},
"radius_PSGF": {
"description": "the radius of convergence of the PSGF"
}
},
"format": "inline"
}
</templatedata>
<includeonly>{{Sandbox other||

[[Category:Mathematics infobox templates|{{PAGENAME}}]]

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