Polynomial Expansions for Solutions of Higher-Order q-Bessel Heat Equation
Mathematical Physics
2022-04-26 v1 math.MP
Abstract
In this paper we give the q-analogue of the higher-order Bessel operators studied by M. I. Klyuchantsev [12] and A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [3]. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs similar to the classical case. Second our goal is to construct the associated q-Fourier transform and the q-analogue of the theory of the heat polynomials introduced by P. C. Rosenbloom and D. V. Widder [13]. Our operator for some value of the vector index generalize the q-j_\alpha Bessel operator of the second order in [4] and a q-Third operator in [6].
Keywords
Cite
@article{arxiv.math-ph/0703026,
title = {Polynomial Expansions for Solutions of Higher-Order q-Bessel Heat Equation},
author = {M. S. Ben Hammouda and Akram Nemri},
journal= {arXiv preprint arXiv:math-ph/0703026},
year = {2022}
}