Formula:KLS:14.12:29

<< Formula:KLS:14.12:28

formula in Little q-Jacobi: Special case

Formula:KLS:14.12:30 >>

${\displaystyle{\displaystyle{\displaystyle\int_{0}^{1}p_{m}\!\left(x|q\right)p_{n}\!\left(x|q\right)\,d_{q}x=(1-q)\sum_{k=0}^{\infty}q^{k}p_{m}\!\left(q^{k}|q\right)p_{n}\!\left(q^{k}|q\right)}}}$

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

${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLegendre
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation in Section 14.12 of KLS.

URL links

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

<< Formula:KLS:14.12:28

formula in Little q-Jacobi: Special case

Formula:KLS:14.12:30 >>