Definition:monicctsqJacobi

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The LaTeX DLMF and DRMF macro \monicctsqJacobi represents the monic continous ${\displaystyle{\displaystyle q}}$ Jacobi polynomial.

This macro is in the category of polynomials.

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

\monicctsqJacobi{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(n,)}_{missing}{}}}}$

\monicctsqJacobi{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(n,@)}_{x}{q}}}}$

\monicctsqJacobi{n}@@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(n,@)}_{@}{x}{q}}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\!\left(x|q\right)=:\frac{2^{n}q^{(\frac{1}{2}\alpha+\frac{1}{4})n}\left(q^{n+\alpha+\beta+1};q\right)_{n}}{\left(q,-q^{\frac{1}{2}(\alpha+\beta+1)},-q^{\frac{1}{2}(\alpha+\beta+2)};q\right)_{n}}{\widehat{P}}^{(\alpha,\beta)}_{n}\!\left(x\right).}}\)\@add@PDF@RDFa@triples\end{document}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(\alpha,\beta)}_{n}}}}$ : monic continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:monicctsqJacobi
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqJacobi
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

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