IF/I[sub.4] Hypergeometric Functions as a Sum of a Product of [sub.2]IF/I[sub.3] Functions

This paper shows that certain[sub.3] F[sub.4] hypergeometric functions can be expanded in sums of pair products of[sub.2] F[sub.3] functions, which reduce in special cases to[sub.2] F[sub.3] functions expanded in sums of pair products of[sub.1] F[sub.2] functions. This expands the class of hypergeom...

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Bibliographic Details
Published inAxioms Vol. 13; no. 3
Main Author Straton, Jack C
Format Journal Article
LanguageEnglish
Published MDPI AG 01.03.2024
Subjects
Functions, Hypergeometric
Mathematical research
United States
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Summary:This paper shows that certain[sub.3] F[sub.4] hypergeometric functions can be expanded in sums of pair products of[sub.2] F[sub.3] functions, which reduce in special cases to[sub.2] F[sub.3] functions expanded in sums of pair products of[sub.1] F[sub.2] functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible as pair-products of generalized Whittaker functions,[sub.2] F[sub.1] functions, and[sub.3] F[sub.2] functions into the realm of[sub.p] F[sub.q] 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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13030203