Finite Bivariate Biorthogonal M-Konhauser Polynomials

2024/09/05 by Esra Güldoğan Lekesız, Lekesiz, Esra Güldoğan, Bayram Çeki̇m +3
Engineering · Mathematics · Physics and Astronomy · #33C45 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2409.03355

openalex publication_date 2024/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct the pair of finite bivariate biorthogonal M-Konhauser polynomials, reduced to the finite orthogonal polynomials M_n^(p,q)(t), by choosing appropriate parameters in order to obtain a relation between the Jacobi Konhauser polynomials and this new finite bivariate biorthogonal polynomials _KM_n;υ^(p,q)(z,t) similar to the relation between the classical Jacobi polynomials P_n^(p,q)(t) and the finite orthogonal polynomials M_n^(p,q)(t). Several properties like generating function, operational/integral representation are derived and some applications like fractional calculus, Fourier transform and Laplace transform are studied thanks to that new transition relation and the definition of finite bivariate M-Konhauser polynomials.

Related

• Finite bivariate biorthogonal I -- Konhauser polynomials
• Finite bivariate biorthogonal N-Konhauser polynomials
• On Bivariate Jacobi Konhauser Polynomials
• Finite biorthogonal polynomials suggested by the finite orthogonal polynomials M_n^(p,q)(x)
• Fractional Calculus Operator Emerging from the 2D Biorthogonal Hermite Konhauser Polynomials