Q Meixner–Pollaczek polynomials - Alchetron, the free social encyclopedia

In mathematics, the q-Meixner–Pollaczek polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by ：

P n ( x ; a ∣ q ) = a − n e i n ϕ a 2 ; q n ( q ; q ) n 3 Φ 2 ( q − n , a e i ( θ + 2 ϕ ) , a e − i θ ; a 2 , 0 ∣ q ; q )

References

Q-Meixner–Pollaczek polynomials Wikipedia

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