Definition:monicctsqJacobi

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The LaTeX DLMF and DRMF macro \monicctsqJacobi represents the monic continous $q$ 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 Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \monicctsqJacobiin 1:31"): {\displaystyle {\displaystyle \monicctsqJacobi{n}}}

\monicctsqJacobi{n}@{x}{q} produces Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \monicctsqJacobiin 1:31"): {\displaystyle {\displaystyle \monicctsqJacobi{n}@{x}{q}}}

\monicctsqJacobi{n}@@{x}{q} produces Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \monicctsqJacobiin 1:31"): {\displaystyle {\displaystyle \monicctsqJacobi{n}@@{x}{q}}}

These are defined by Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \ctsqJacobiin 2:1"): {\displaystyle {\displaystyle \ctsqJacobi{\alpha}{\beta}{n}@{x}{q}=:\frac{2^nq^{(\frac{1}{2}\alpha+\frac{1}{4})n}\qPochhammer{q^{n+\alpha+\beta+1}}{q}{n}} {\qPochhammer{q,-q^{\frac{1}{2}(\alpha+\beta+1)},-q^{\frac{1}{2}(\alpha+\beta+2)}}{q}{n}}\monicctsqJacobi{\alpha}{\beta}{n}@@{x}{q}. }

Symbols List

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

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