Some generating functions of the Bessel and related orthogonal polynomials
Applicable Nonlinear Analysis, Volume 1, Issue 1, June 2024, Pages: 1–19
HARI MOHAN SRIVASTAVA
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
Abstract
Our main object in this article is to present several families of generating functions for the simple Bessel polynomials \(\mathfrak y_n(x)\) and the generalized Bessel polynomials \(\mathfrak y_n(x; α, β)\). We also investigate and present various potentially useful generating-function relationships involving such other orthogonal polynomial systems as (for example) the Jacobi, Laguerre and Hermite polynomials, together with their specialized and parametrically-varied forms.
Cite this Article as
Hari Mohan Srivastava, Some generating functions of the Bessel and related orthogonal polynomials,Applicable Nonlinear Analysis, 1 (2024), 1–19