₃F₄ Hypergeometric Functions as a Sum of a Product of ₂F₃ Functions

Authors

Jack C. Straton, Portland State UniversityFollow

Published In

Axioms

Document Type

Article

Publication Date

3-2024

Subjects

Hypergeometric functions

Abstract

This paper shows that certain ₃F₄ hypergeometric functions can be expanded in sums of pair products of ₂F₃ functions, which reduce in special cases to ₂F₃ functions expanded in sums of pair products of ₁F₂ functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible as pair-products of generalized Whittaker functions, ₂F₁ functions, and ₃F₂ functions into the realm of pFq functions where p < q for both the summand and terms in the series. In addition to its intrinsic value, this result has a specific application in calculating the response of the atoms to laser stimulation in the Strong Field Approximation.

Rights

Copyright: © 2024 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/).

Locate the Document

https://doi.org/10.3390/axioms13030203

DOI

10.3390/axioms13030203

Persistent Identifier

https://archives.pdx.edu/ds/psu/41449

Citation Details

Straton, J. C. (2024). 3 F 4 Hypergeometric Functions as a Sum of a Product of 2 F 3 Functions. Axioms, 13(3), 203.