Formula:KLS:14.09:18

<< Formula:KLS:14.09:17

formula in q-Meixner-Pollaczek

Formula:KLS:14.09:19 >>

${\displaystyle{\displaystyle{\displaystyle\left|\frac{\left(a{\mathrm{e}^{\mathrm{i}\phi}}t;q\right)_{\infty}}{\left({\mathrm{e}^{\mathrm{i}(\theta+\phi)}}t;q\right)_{\infty}}\right|^{2}{}=\sum_{n=0}^{\infty}P_{n}\!\left(x;a|q\right)t^{n}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner-Pollaczek polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixnerPollaczek

Bibliography

Equation in Section 14.9 of KLS.

URL links

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

<< Formula:KLS:14.09:17

formula in q-Meixner-Pollaczek

Formula:KLS:14.09:19 >>