Formula:KLS:09.07:13

<< Formula:KLS:09.07:12

formula in Meixner-Pollaczek

Formula:KLS:09.07:14 >>

${\displaystyle{\displaystyle{\displaystyle(1-{\mathrm{e}^{\mathrm{i}\phi}}t)^{-\lambda+\mathrm{i}x}(1-{\mathrm{e}^{-\mathrm{i}\phi}}t)^{-\lambda-\mathrm{i}x}=\sum_{n=0}^{\infty}P^{(\lambda)}_{n}\!\left(x;\phi\right)t^{n}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : 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
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}}}}$ : Meixner-Pollaczek polynomial : http://dlmf.nist.gov/18.19#P3.p1

Bibliography

Equation in Section 9.7 of KLS.

URL links

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<< Formula:KLS:09.07:12

formula in Meixner-Pollaczek

Formula:KLS:09.07:14 >>