Formula:KLS:14.24:03

<< Formula:KLS:14.24:02

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:04 >>

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

Proof

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Symbols List

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

Bibliography

Equation in Section 14.24 of KLS.

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<< Formula:KLS:14.24:02

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:04 >>