Template:Infobox combinatorial classes/doc: Difference between revisions

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Latest revision as of 01:21, 18 January 2023

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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:

Script error: No such module "Parameter names example".

{{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 <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

Click here to see a monthly parameter usage report for this template based on this TemplateData.

TemplateData for Infobox combinatorial classes

No description.

Template parameters

This template prefers inline formatting of parameters.

ParameterDescriptionTypeStatus
box_widthbox_width

no description

Unknownoptional
Namename

Name at the top of the infobox; should be the name of the sequence, without the word sequence

Example
Fibonnacci
Unknownoptional
notationnotation

no description

Unknownoptional
introintro

no description

Unknownoptional
parametersparameters

no description

Unknownoptional
supportsupport

Where the sequence is defined and non-zero.

Example
The even numbers. The prime numbers
Unknownoptional
nth elementnth element

no description

Unknownoptional
asymptoticasymptotic

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
Unknownoptional
OGFOGF

The ordinary generating function of the sequence

Unknownoptional
its radiusradius_OGF

radius of convergence of the OGF

Example
1
Numberoptional
EGFEGF

The exponential generating function of the sequence

Unknownoptional
radius_EGFradius_EGF

the radius of convergence of the EGF

Unknownoptional
PGFPGF

The poisson generating function of the sequence

Unknownoptional
radius_PGFradius_PGF

the radius of convergence of the PGF

Unknownoptional
LSLS

The Lambert series of the sequence

Unknownoptional
radius_LSradius_LS

the radius of convergence of the LS

Unknownoptional
BSBS

The Bell series of the sequence

Unknownoptional
radius_BSradius_BS

the radius of convergence of the BS

Unknownoptional
DGFDGF

The Dirichlet series generating functions of the sequence

Unknownoptional
radius_DGFradius_DGF

the radius of convergence of the DGF

Unknownoptional
PSGFPSGF

The Polynomial Sequence Generating Function of the sequence

Unknownoptional
radius_PSGFradius_PSGF

the radius of convergence of the PSGF

Unknownoptional