Formula:KLS:14.25:04

<< Formula:KLS:14.25:03

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:05 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{V}}^{(n)}_{\alpha}}}}$ : monic Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:monicAlSalamCarlitzII

Bibliography

Equation in Section 14.25 of KLS.

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<< Formula:KLS:14.25:03

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:05 >>