Formula:KLS:14.24:06

<< Formula:KLS:14.24:05

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:08 >>

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

Substitution(s)

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

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.

URL links

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<< Formula:KLS:14.24:05

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:08 >>