Formula:KLS:14.12:30

<< Formula:KLS:14.12:29

formula in Little q-Jacobi: Special case

Formula:KLS:14.12:31 >>

${\displaystyle{\displaystyle{\displaystyle\int_{0}^{1}p_{m}\!\left(x|q\right)p_{n}\!\left(x|q\right)\,d_{q}x=\frac{(1-q)q^{n}}{(1-q^{2n+1})}\,\delta_{m,n}}}}$

Proof

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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
${\displaystyle{\displaystyle{\displaystyle\delta_{m,n}}}}$ : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4

Bibliography

Equation in Section 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:29

formula in Little q-Jacobi: Special case

Formula:KLS:14.12:31 >>