Formula:KLS:09.07:04

<< Formula:KLS:09.07:03

formula in Meixner-Pollaczek

Formula:KLS:09.07:05 >>

${\displaystyle{\displaystyle{\displaystyle x{\widehat{P}}^{(\lambda)}_{n}\!\left(x\right)={\widehat{P}}^{(\lambda)}_{n+1}\!\left(x\right)-\left(\frac{n+\lambda}{\tan\phi}\right){\widehat{P}}^{(\lambda)}_{n}\!\left(x\right)+\frac{n(n+2\lambda-1)}{4{\sin^{2}}\phi}{\widehat{P}}^{(\lambda)}_{n-1}\!\left(x\right)}}}$

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

${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(\alpha)}_{n}}}}$ : monic Meixner-Pollaczek polynomial : http://drmf.wmflabs.org/wiki/Definition:monicMeixnerPollaczek
${\displaystyle{\displaystyle{\displaystyle\mathrm{tan}}}}$ : tangent function : http://dlmf.nist.gov/4.14#E4
${\displaystyle{\displaystyle{\displaystyle\mathrm{sin}}}}$ : sine function : http://dlmf.nist.gov/4.14#E1

Bibliography

Equation in Section 9.7 of KLS.

URL links

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

<< Formula:KLS:09.07:03

formula in Meixner-Pollaczek

Formula:KLS:09.07:05 >>