A hypergeometric sequence of biorthogonal polynomials and its relationship with Meixner-Pollaczek polynomials

2025/10/14 by Masjed-Jamei, Mohammad, Saad, Nasser
#Fourier transform #Generalized Laguerre polynomials #Hypergeometric series #Meixner-Pollaczek polynomials #Parseval identity

paper · doi:10.57647/j.jtap.2025.1904.38

Abstract

Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. In this paper, based on generalized Laguerre polynomials, we introduce a new sequence of biorthogonal hypergeometric polynomials and obtain its orthogonality relation explicitly. In this sense, we also recall some similar results available in the literature as the sequence introduced in this work is the last one for classical cases.

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