Formula:KLS:14.05:47

<< Formula:KLS:14.05:46

formula in Big q-Jacobi

Formula:KLS:14.05:48 >>

${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(-d/(qb);a,b,c,d;q\right)=\left(-\frac{ad}{bc}\right)^{n}\frac{\left(qb,-qbc/d;q\right)_{n}}{\left(qa,-qad/c;q\right)_{n}}}}}$

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
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:46

formula in Big q-Jacobi

Formula:KLS:14.05:48 >>