₃F₄ hypergeometric functions as a sum of a product of ₂F₃ functions

2024/12/29 by Straton, Jack C.
#33C05 #33C10 #33D50 #33F10 #41A10 #42C10 #65D20 #68W30 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2501.06206

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. 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 _pF_q functions where p

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