Formula:KLS:09.04:27

<< Formula:KLS:09.04:26

formula in Continuous Hahn

Formula:KLS:09.05:01 >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a,a+\frac{1}{2},a,a+\frac{1}{2}\right)=\frac{{\left(2a\right)_{n}}{\left(2a+\frac{1}{2}\right)_{n}}}{{\left(4a\right)_{n}}}P^{(2a)}_{n}\!\left(2x;\frac{1}{2}\pi\right)}}}$

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

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : continuous Hahn polynomial : http://dlmf.nist.gov/18.19#P2.p1
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}}}}$ : Meixner-Pollaczek polynomial : http://dlmf.nist.gov/18.19#P3.p1

Bibliography

Equation in Section 9.4 of KLS.

URL links

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

<< Formula:KLS:09.04:26

formula in Continuous Hahn

Formula:KLS:09.05:01 >>