Formula:KLS:14.04:08

<< Formula:KLS:14.04:07

formula in Continuous q-Hahn

Formula:KLS:14.04:11 >>

${\displaystyle{\displaystyle{\displaystyle{\tilde{p}}_{n}\!\left(x\right):={\tilde{p}}_{n}\!\left(x;a,b,c,d;q\right)=\frac{(a{\mathrm{e}^{\mathrm{i}\phi}})^{n}p_{n}\!\left(x;a,b,c,d;q\right)}{\left(ab{\mathrm{e}^{2\mathrm{i}\phi}},ac,ad;q\right)_{n}}}}}$

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

${\displaystyle{\displaystyle{\displaystyle{\tilde{p}}_{n}}}}$ : normalized continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial ${\displaystyle{\displaystyle{\displaystyle{\tilde{p}}}}}$ : http://drmf.wmflabs.org/wiki/Definition:normctsqHahnptilde
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : 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
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqHahn
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.4 of KLS.

URL links

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

<< Formula:KLS:14.04:07

formula in Continuous q-Hahn

Formula:KLS:14.04:11 >>