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/).
DOI
10.3390/math13030421
Persistent Identifier
https://archives.pdx.edu/ds/psu/42998
Citation Details
Straton, J. C. (2025). 3F4 Hypergeometric Functions as a Sum of a Product of 1F2 Functions. Mathematics, 13(3), 421. https://doi.org/10.3390/math13030421
Description
MSC: 33C10; 42C10; 41A10; 33F10; 65D20; 68W30; 33D50; 33C05