Definition:monicctsqUltra

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The LaTeX DLMF and DRMF macro \monicctsqUltra represents the monic continuous ${\displaystyle{\displaystyle q}}$ ultraspherical Rogers polynomial.

This macro is in the category of polynomials.

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

\monicctsqUltra{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}}}}$

\monicctsqUltra{n}@{x}{\beta}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}\!\left(x;\beta\,|\,q\right)}}}$

\monicctsqUltra{n}@@{x}{\beta}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}\!\left(x\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle C_{n}\!\left(x;\beta\,|\,q\right)=:\frac{2^{n}\left(\beta;q\right)_{n}}{\left(q;q\right)_{n}}{\widehat{C}}_{n}\!\left(x\right).}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}}}}$ : monic continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-ultraspherical/Rogers polynomial : http://drmf.wmflabs.org/wiki/Definition:monicctsqUltra
${\displaystyle{\displaystyle{\displaystyle C_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-ultraspherical/Rogers polynomial : http://dlmf.nist.gov/18.28#E13
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

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