Finite bivariate biorthogonal I -- Konhauser polynomials
Classical Analysis and ODEs
2025-11-27 v2
Abstract
In this paper, a finite set of biorthogonal polynomials in two variables is produced using Konhauser polynomials. Some properties containing operational and integral representation, Laplace transform, fractional calculus operators of this family are studied. Also, computing Fourier transform for the new set, a new family of biorthogonal functions are derived via Parseval's identity. On the other hand, this finite set is modified by adding two new parameters in order to have semigroup property and construct fractional calculus operators. Further, integral equation and integral operator are also derived for the modified version.
Cite
@article{arxiv.2408.07811,
title = {Finite bivariate biorthogonal I -- Konhauser polynomials},
author = {Esra Güldoğan Lekesiz and Bayram Çekim and Mehmet Ali Özarslan},
journal= {arXiv preprint arXiv:2408.07811},
year = {2025}
}