Formula:KLS:14.18:10

<< Formula:KLS:14.18:09

formula in Continuous big q-Hermite

Formula:KLS:14.18:11 >>

${\displaystyle{\displaystyle{\displaystyle x{\widehat{H}}_{n}\!\left(x\right)={\widehat{H}}_{n+1}\!\left(x\right)+\frac{1}{2}aq^{n}{\widehat{H}}_{n}\!\left(x\right)+\frac{1}{4}(1-q^{n}){\widehat{H}}_{n-1}\!\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{H}}_{n}}}}$ : monic continuous big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite polynomial : http://drmf.wmflabs.org/wiki/Definition:monicctsbigqHermite

Bibliography

Equation in Section 14.18 of KLS.

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formula in Continuous big q-Hermite

Formula:KLS:14.18:11 >>