Formula:KLS:14.05:07

<< Formula:KLS:14.05:06

formula in Big q-Jacobi

Formula:KLS:14.05:08 >>

${\displaystyle{\displaystyle{\displaystyle\bigqJacobi{n}@{x}{a}{b}{c}{q}=\frac{\qPochhammer{abq^{n+1}}{q}{n}}{\qPochhammer{aq,cq}{q}{n}}\monicbigqJacobi{n}@@{x}{a}{b}{c}{q}}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqJacobi
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}_{n}}}}$ : monic big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:monicbigqJacobi

Bibliography

Equation in Section 14.5 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.05:06

formula in Big q-Jacobi

Formula:KLS:14.05:08 >>