Definition:monicUltra

<< Definition:monicStieltjesWigert

Main Page

Definition:monicWilson >>

The LaTeX DLMF and DRMF macro \monicUltra represents the monic ultraspherical Gegenbauer polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\monicUltra{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}^{n}_{}}}}$

\monicUltra{n}@{x} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}^{n}_{@}{x}}}}$

\monicUltra{n}@@{x} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}^{n}_{@}\left(x\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle C^{\lambda}_{n}\left(x\right)=:\frac{2^{n}{\left(\lambda\right)_{n}}}{n!}{\widehat{C}}^{\lambda}_{n}\left(x\right).}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}^{\mu}_{n}}}}$ : monic ultraspherical/Gegenbauer polynomial : http://drmf.wmflabs.org/wiki/Definition:monicUltra
${\displaystyle{\displaystyle{\displaystyle C^{\mu}_{n}}}}$ : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

<< Definition:monicStieltjesWigert

Main Page

Definition:monicWilson >>