# Generalized Meixner-Pollaczek polynomials

Abstract: We consider the generalized Meixner-Pollaczek (GMP) polynomials P λ (x; θ , ψ )o f a variable x ∈ R and parameters λ >0 ,θ ∈ (0, π ), ψ ∈ R ,d ef inedvia the generating function

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### Additional excerpts

...1: Kanas and Tatarczak [28] studied the generalized Meixner-Pollaczek polynomials Qn(x; θ ,ψ) generated by ∞ ∑ n=0 Qλn (x; θ ,ψ) t n = (1 − t eiθ )−λ+ix (1 − t eiψ)−λ−ix (|t| < 1; λ > 0, θ ∈ (0,π) , ψ ∈ R) ....

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...[28] Kanas S, Tatarczak A. Generalized Meixner-Pollaczek polynomials....

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...Remark 5.1: Kanas and Tatarczak [28] studied the generalized Meixner-Pollaczek polynomials Qλn(x; θ ,ψ) generated by ∞∑ n=0 Qλn (x; θ ,ψ) t n = (1 − t eiθ )−λ+ix (1 − t eiψ)−λ−ix (|t| < 1; λ > 0, θ ∈ (0,π) , ψ ∈ R) ....

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