# Definition:monicctsqJacobi

The LaTeX DLMF and DRMF macro \monicctsqJacobi represents the monic continous ${\displaystyle q}$ 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 $\displaystyle {\displaystyle \monicctsqJacobi{n}}$
\monicctsqJacobi{n}@{x}{q} produces $\displaystyle {\displaystyle \monicctsqJacobi{n}@{x}{q}}$
\monicctsqJacobi{n}@@{x}{q} produces $\displaystyle {\displaystyle \monicctsqJacobi{n}@@{x}{q}}$

These are defined by $\displaystyle {\displaystyle \ctsqJacobi{\alpha}{\beta}{n}@{x}{q}=:\frac{2^nq^{(\frac{1}{2}\alpha+\frac{1}{4})n}\qPochhammer{q^{n+\alpha+\beta+1}}{q}{n}} {\qPochhammer{q,-q^{\frac{1}{2}(\alpha+\beta+1)},-q^{\frac{1}{2}(\alpha+\beta+2)}}{q}{n}}\monicctsqJacobi{\alpha}{\beta}{n}@@{x}{q}.$

## Symbols List

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