Formula:KLS:14.05:34

<< Formula:KLS:14.05:33

formula in Big q-Jacobi

Formula:KLS:14.05:35 >>

${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x;a,b,c,d;q\right)=\qHyperrphis{3}{2}@@{q^{-n},q^{n+1}ab,qac^{-1}x}{qa,-qac^{-1}d}{q}{q}}}}$

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
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.5 of KLS.

URL links

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formula in Big q-Jacobi

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