Formula:KLS:14.12:07

<< Formula:KLS:14.12:06

formula in Little q-Jacobi

Formula:KLS:14.12:08 >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a,b;q\right)=\frac{(-1)^{n}q^{-\binomial{n}{2}}\left(abq^{n+1};q\right)_{n}}{\left(aq;q\right)_{n}}{\widehat{p}}_{n}\!\left(x\right)}}}$

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

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}}}}$ : monic little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:moniclittleqJacobi

Bibliography

Equation in Section 14.12 of KLS.

URL links

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

<< Formula:KLS:14.12:06

formula in Little q-Jacobi

Formula:KLS:14.12:08 >>