Formula:KLS:14.05:31

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formula in Big q-Jacobi

Formula:KLS:14.05:32 >>

${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x;a,b,c,d;q\right)=P_{n}\!\left(ac^{-1}qx;a,b,-ac^{-1}d;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqJacobi

Bibliography

Equation in Section 14.5 of KLS.

URL links

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formula in Big q-Jacobi

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