Formula:KLS:14.25:14

<< Formula:KLS:14.25:13

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:15 >>

${\displaystyle{\displaystyle{\displaystyle\frac{\left(xt;q\right)_{\infty}}{\left(t,at;q\right)_{\infty}}=\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binomial{n}{2}}}{\left(q;q\right)_{n}}V^{(a)}_{n}\!\left(x;q\right)t^{n}}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle V^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII

Bibliography

Equation in Section 14.25 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.25:13

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:15 >>