Meixner–Pollaczek polynomials

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Not to be confused with Meixner polynomials.

In mathematics, the Meixner–Pollaczek polynomials are a family of orthogonal polynomials P(λ)
n
(x,φ) introduced by Meixner (1934), which up to elementary changes of variables are the same as the Pollaczek polynomials Pλ
n
(x,a,b) rediscovered by Pollaczek (1949) in the case λ=1/2, and later generalized by him.

They are defined by

They are orthogonal on the real line with respect to the weight function

and the orthogonality is given by

See also[edit]

References[edit]