Work

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx

Year: 2026

Type: article

Abstract: ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature. In this paper, we derive for the first time a pair of finite univariate biorthogonal polynomials suggested by the finite univariate orthogonal polynomials . The corresponding biorthogonality relation and some useful relations and properties, including 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 the new biorthogonal polynomial set .

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70696

Author: Esra Güldoğan Lekesiz

Institution: Çankaya University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,000

Funder: Türkiye Bilimsel ve Teknolojik Araştırma Kurumu