Formula:KLS:14.24:14

<< Formula:KLS:14.24:13

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:15 >>

${\displaystyle{\displaystyle{\displaystyle\frac{\left(t,at;q\right)_{\infty}}{\left(xt;q\right)_{\infty}}=\sum_{n=0}^{\infty}\frac{U^{(a)}_{n}\!\left(x;q\right)}{\left(q;q\right)_{n}}t^{n}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle U^{(n)}_{\alpha}}}}$ : 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:14.24:13

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:15 >>