Polynomial Expansions for Solutions of Higher-order q-Bessel Heat Equation
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Abstract
[[abstract]]In this paper we give the q-analogue of the higher-order Bessel opera-
tors 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 Bessel operator of the second order
in [4] and a q-Third operator in [6]