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Polynomial Expansions for Solutions of Higher-Order q-Bessel Heat Equation

M. S. Ben Hammouda·Akram Nemri
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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].

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M. S. Ben Hammouda, Akram Nemri. 2007-03-08. Polynomial Expansions for Solutions of Higher-Order q-Bessel Heat Equation. https://arxiv.org/abs/math-ph/0703026

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