Formula:KLS:14.12:12

<< Formula:KLS:14.12:08

formula in Little q-Jacobi

Formula:KLS:14.12:13 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi

Bibliography

Equation in Section 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:08

formula in Little q-Jacobi

Formula:KLS:14.12:13 >>