This template uses TemplateStyles: |
Usage edit
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:
{{{intro}}} | |
Parameters | {{{parameters}}} |
---|---|
Support | {{{support}}} |
Asymptotic | {{{asymptotic}}} |
Ordinary generating function | {{{OGF}}} |
radius of convergence of the OGF | {{{OGF radius}}} |
Exponential generating function | {{{EGF}}} |
its radius | {{{EGF radius}}} |
Poisson generating function | {{{PGF}}} |
Lambert series | {{{LS}}} |
its radius | {{{LS radius}}} |
Bell series | {{{BS}}} |
its radius | {{{BS radius}}} |
Dirichlet series generating function | {{{DGF}}} |
Polynomial sequence generating function | {{{PSGF}}} |
its radius | {{{PSGF radius}}} |
{{{PGF radius}}} |
{{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 edit
- 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 -th element) is usually denoted. For example, 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 -th element of the sequence. (e.g. for fibonnaci number, it would be )
- asymptotic — A function with the same domain than the sequence, which is asymptotically equivalent to it. (e.g. for fibonnaci number, it would be )
- 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 edit
TemplateData for Infobox combinatorial classes
No description.
Parameter | Description | Type | Status | |
---|---|---|---|---|
box_width | box_width | no description | Unknown | optional |
Name | name | Name at the top of the infobox; should be the name of the sequence, without the word sequence
| Unknown | optional |
notation | notation | no description | Unknown | optional |
intro | intro | no description | Unknown | optional |
parameters | parameters | no description | Unknown | optional |
support | support | Where the sequence is defined and non-zero.
| Unknown | optional |
nth element | nth element | no description | Unknown | optional |
asymptotic | asymptotic | A function with the same domain than the sequence, which is asymptotically equivalent to it.
| Unknown | optional |
OGF | OGF | The ordinary generating function of the sequence | Unknown | optional |
its radius | radius_OGF | radius of convergence of the OGF
| Number | optional |
EGF | EGF | The exponential generating function of the sequence | Unknown | optional |
radius_EGF | radius_EGF | the radius of convergence of the EGF | Unknown | optional |
PGF | PGF | The poisson generating function of the sequence | Unknown | optional |
radius_PGF | radius_PGF | the radius of convergence of the PGF | Unknown | optional |
LS | LS | The Lambert series of the sequence | Unknown | optional |
radius_LS | radius_LS | the radius of convergence of the LS | Unknown | optional |
BS | BS | The Bell series of the sequence | Unknown | optional |
radius_BS | radius_BS | the radius of convergence of the BS | Unknown | optional |
DGF | DGF | The Dirichlet series generating functions of the sequence | Unknown | optional |
radius_DGF | radius_DGF | the radius of convergence of the DGF | Unknown | optional |
PSGF | PSGF | The Polynomial Sequence Generating Function of the sequence | Unknown | optional |
radius_PSGF | radius_PSGF | the radius of convergence of the PSGF | Unknown | optional |