3 F 4 Hypergeometric Functions as a Sum of a Product of 1 F 2 Functions

Jack C. Straton ()
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Jack C. Straton: Department of Physics, Portland State University, Portland, OR 97207-0751, USA

Mathematics, 2025, vol. 13, issue 3, 1-12

Abstract: This paper shows that certain F 4 3 hypergeometric functions can be expanded in sums of pair products of F 2 1 functions. In special cases, the F 4 3 hypergeometric functions reduce to F 3 2 functions. Further special cases allow one to reduce the F 3 2 functions to F 2 1 functions, and the sums to products of F 1 0 (Bessel) and F 2 1 functions. The class of hypergeometric functions with summation theorems are thereby expanded beyond those expressible as pair-products of F 1 2 functions, F 2 3 functions, and generalized Whittaker functions, into the realm of F q p functions where p < q for both the summand and terms in the series.

Keywords: 3 F 4 hypergeometric functions; 2 F 3 hypergeometric functions; 1 F 2 hypergeometric functions; Bessel functions; Strong Field Approximation; laser stimulation; summation theorem; Fourier–Legendre series expansions; Chebyshev series expansions; Gegenbauer series expansions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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