Formula:KLS:14.05:14

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formula in Big q-Jacobi

Formula:KLS:14.05:15 >>

${\displaystyle{\displaystyle{\displaystyle(x-a)(x-c)P_{n}\!\left(x;a,b,c;q\right)-a(x-1)(bx-c)P_{n}\!\left(qx;a,b,c;q\right){}=(1-a)(1-c)xP_{n+1}\!\left(x;aq^{-1},bq^{-1},cq^{-1};q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : 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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