Formula:KLS:14.05:51

<< Formula:KLS:14.05:50

formula in Big q-Jacobi

Formula:KLS:14.05:52 >>

${\displaystyle{\displaystyle{\displaystyle P_{2n+1}\!\left(x;a,a,1,1;q\right)=\frac{qaxp_{n}\!\left(x^{2};q,a^{2};q^{2}\right)}{p_{n}\!\left((qa)^{-2};q,a^{2};q^{2}\right)}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial with four parameters : http://drmf.wmflabs.org/wiki/Definition:bigqJacobiIVparam
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:50

formula in Big q-Jacobi

Formula:KLS:14.05:52 >>