Template:Infobox combinatorial classes/doc

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:

{{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 =
}}

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 $n$-th element) is usually denoted. For example, $n!$ 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 $n$-th element of the sequence. (e.g. for fibonnaci number, it would be $\frac{1}{\sqrt{5}}({\left(\frac{1+\sqrt{5}}{2}\right)}^n+{\left(\frac{1-\sqrt{5}}{2}\right)}^n)$)
• asymptotic — A function with the same domain than the sequence, which is asymptotically equivalent to it. (e.g. for fibonnaci number, it would be $\frac{1}{\sqrt{5}}\left({\left(\frac{1+\sqrt{5}}{2}\right)}^n\right)$)
• 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

Template:TemplateData header <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": "Failed to parse (syntax error): {\displaystyle \\frac{1}{\\sqrt5}\\left(\\left(\\frac{1+\\sqrt 5}{2}\\right)^n\\right)} 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>