Published In

Mathematics

Document Type

Article

Publication Date

1-27-2025

Subjects

Bessel functions, Hypergeometric functions

Abstract

This paper shows that certain 3F4 hypergeometric functions can be expanded in sums of pair products of 1F2 functions. In special cases, the 3F4 hypergeometric functions reduce to 2F3 functions. Further special cases allow one to reduce the 2F3 functions to 1F2 functions, and the sums to products of 0F1 (Bessel) and 1F2 functions. The class of hypergeometric functions with summation theorems are thereby expanded beyond those expressible as pair-products of 2F1 functions, 3F2 functions, and generalized Whittaker functions, into the realm of pFq functions where p < q for both the summand and terms in the series.

Rights

© 2025 by the author. Licensee MDPI, Basel, Switzerland. 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/).

Description

MSC: 33C10; 42C10; 41A10; 33F10; 65D20; 68W30; 33D50; 33C05

DOI

10.3390/math13030421

Persistent Identifier

https://archives.pdx.edu/ds/psu/42998

Included in

Physics Commons

Share

COinS