Finite biorthogonal polynomials suggested by the finite orthogonal polynomials M_n^(p,q)(x)

2024/08/23 by Esra Güldoğan Lekesız, Lekesiz, Esra Güldoğan · 1 citation
Mathematics · #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2408.15010

openalex publication_date 2024/08/23 · openalex created_date 2024/09/21 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive a pair of finite univariate biorthogonal polynomials suggested by the finite univariate orthogonal polynomials M_n^(p,q)(x). The corresponding biorthogonality relation is given. Some useful relations and properties, concluding differential equation and generating function, are presented. Further, a new family of finite biorthogonal functions is obtained using Fourier transform and Parseval identity. In addition, we compute the Laplace transform and fractional calculus operators for polynomials M_n(p,q,υ;x).

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