Formula:KLS:14.25:06

<< Formula:KLS:14.25:05

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:08 >>

${\displaystyle{\displaystyle{\displaystyle-(1-q^{n})x^{2}y(x){}=(1-x)(a-x)y(qx)-\left[(1-x)(a-x)+aq\right]y(x)+aqy(q^{-1}x)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle y(x)=V^{(a)}_{n}\!\left(x;q\right)}}}$

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.

URL links

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<< Formula:KLS:14.25:05

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:08 >>