Formula:KLS:14.04:28

<< Formula:KLS:14.04:27

formula in Continuous q-Hahn

Formula:KLS:14.05:01 >>

${\displaystyle{\displaystyle{\displaystyle\littleqJacobi{n}@{x}{a}{b}{q}:=\AskeyWilson{n}@{x}{a\expe^{\iunit\phi}}{b\expe^{\iunit\phi}}{a\expe^{-\iunit\phi}}{b\expe^{-\iunit\phi}}{q}(x=\cos\!\left(\theta+\phi\right))}}}$

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

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : Askey-Wilson polynomial : http://dlmf.nist.gov/18.28#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : 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
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2

Bibliography

Equation in Section 14.4 of KLS.

URL links

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

<< Formula:KLS:14.04:27

formula in Continuous q-Hahn

Formula:KLS:14.05:01 >>