Formula:KLS:14.09:17

<< Formula:KLS:14.09:16

formula in q-Meixner-Pollaczek

Formula:KLS:14.09:18 >>

${\displaystyle{\displaystyle{\displaystyle\left|\frac{\left(a{\mathrm{e}^{\mathrm{i}\phi}}t;q\right)_{\infty}}{\left({\mathrm{e}^{\mathrm{i}(\theta+\phi)}}t;q\right)_{\infty}}\right|^{2}{}=\frac{\left(a{\mathrm{e}^{\mathrm{i}\phi}}t,a{\mathrm{e}^{-\mathrm{i}\phi}}t;q\right)_{\infty}}{\left({\mathrm{e}^{\mathrm{i}(\theta+\phi)}}t,{\mathrm{e}^{-\mathrm{i}(\theta+\phi)}}t;q\right)_{\infty}}}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle x=\cos\left(\theta+\phi\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : 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 14.9 of KLS.

URL links

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