Formula:KLS:14.05:12

<< Formula:KLS:14.05:08

formula in Big q-Jacobi

Formula:KLS:14.05:13 >>

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

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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