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arXiv · 2403.19664

$\,_{3}F_{4}$ hypergeometric functions as a sum of a product of $\,_{2}F_{3}$ functions

Jack C. Straton
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Abstract

This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions may be expanded in sums of pair products of $\,_{2}F_{3}$ functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible as pair-products of generalized Whittaker functions, $\,_{2}F_{1}$ functions, and $\,_{3}F_{2}$ functions into the realm of $\,_{P}F_{Q}$ 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.

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Jack C. Straton. 2024-02-07. $\,_{3}F_{4}$ hypergeometric functions as a sum of a product of $\,_{2}F_{3}$ functions. https://arxiv.org/abs/2403.19664

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