Formula:KLS:14.25:03

<< Formula:KLS:14.25:02

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:04 >>

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

Proof

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Symbols List

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

Bibliography

Equation in Section 14.25 of KLS.

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<< Formula:KLS:14.25:02

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:04 >>