Definition:ctsqJacobi

The LaTeX DLMF and DRMF macro \ctsqJacobi represents the continuous $q$ -Jacobi polynomial.

This macro is in the category of polynomials.

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

\ctsqJacobi{\alpha}{\beta}{m} produces $\displaystyle \ctsqJacobi{\alpha}{\beta}{m}$
\ctsqJacobi{\alpha}{\beta}{m}@{x}{q} produces $\displaystyle \ctsqJacobi{\alpha}{\beta}{m}@{x}{q}$

These are defined by
$\displaystyle \ctsqJacobi{\alpha}{\beta}{n}@{x}{q} :=\frac{\qPochhammer{q^{\alpha+1}}{q}{n}}{\qPochhammer{q}{q}{n}} \qHyperrphis{4}{3}@@{q^{-n},q^{n+\alpha+\beta+1},q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{i\theta},q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{-i\theta}} {q^{\alpha+1},-q^{\frac{1}{2}(\alpha+\beta+1)},-q^{\frac{1}{2}(\alpha+\beta+2)}}{q}{q}$

with $\displaystyle x=\cos@@{\theta}$ .

Symbols List

$P_{n}^{(\alpha ,\beta )}}$ : continuous $q}$ -Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqJacobi
$(a;q)_{n}}$ : $q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${{}_{r}\phi _{s}}}$ : basic hypergeometric (or $q}$ -hypergeometric) function : http://dlmf.nist.gov/17.4#E1
$\mathrm {e} }$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
$\mathrm {cos} }$ : cosine function : http://dlmf.nist.gov/4.14#E2