Formula:KLS:09.07:03

<< Formula:KLS:09.07:02

formula in Meixner-Pollaczek

Formula:KLS:09.07:04 >>

${\displaystyle{\displaystyle{\displaystyle(n+1)P^{(\lambda)}_{n+1}\!\left(x;\phi\right)-2\left[x\sin\phi+(n+\lambda)\cos\phi\right]P^{(\lambda)}_{n}\!\left(x;\phi\right){}+(n+2\lambda-1)P^{(\lambda)}_{n-1}\!\left(x;\phi\right)=0}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}}}}$ : Meixner-Pollaczek polynomial : http://dlmf.nist.gov/18.19#P3.p1
${\displaystyle{\displaystyle{\displaystyle\mathrm{sin}}}}$ : sine function : http://dlmf.nist.gov/4.14#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2

Bibliography

Equation in Section 9.7 of KLS.

URL links

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<< Formula:KLS:09.07:02

formula in Meixner-Pollaczek

Formula:KLS:09.07:04 >>