Published In
Mathematics
Document Type
Article
Publication Date
12-21-2024
Abstract
Summation of infinite series has played a significant role in a broad range of problems in the physical sciences and is of interest in a purely mathematical context. In a prior paper, we found that the Fourier–Legendre series of a Bessel function of the first kind JN(kx) and modified Bessel functions of the first kind IN(kx) lead to an infinite set of series involving 1F2 hypergeometric functions (extracted therefrom) that could be summed, having values that are inverse powers of the eight primes 1/ ( 2i 3j 5k 7l 11m 13n 17o19p ) multiplying powers of the coefficient k, for the first 22 terms in each series. The present paper shows how to generate additional, doubly infinite summed series involving 1F2 hypergeometric functions from Chebyshev polynomial expansions of Bessel functions, and trebly infinite sets of summed series involving 1F2 hypergeometric functions from Gegenbauer polynomial expansions of Bessel functions. That the parameters in these new cases can be varied at will significantly expands the landscape of applications for which they could provide a solution.
Rights
Copyright: © 2024 by the author. Licensee MDPI, Basel, Switzerland.
DOI
10.3390/math12244016
Persistent Identifier
https://archives.pdx.edu/ds/psu/42918
Citation Details
Straton, J. C. (2024). Summed Series Involving 1 F 2 Hypergeometric Functions. Mathematics, 12(24), 1-19.
Description
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).