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

Jack C. Straton

doi:10.3390/math13030421

paper

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

arXiv:2501.06206 · doi:10.3390/math13030421

Abstract

This paper shows that certain $_{3} F_{4}$ hypergeometric functions can be expanded in sums of pair products of $_{1} F_{2}$ functions. In special cases, the $_{3} F_{4}$ hypergeometric functions reduce to $_{2} F_{3}$ functions. Further special cases allow one to reduce the $_{2} F_{3}$ functions to $_{1} F_{2}$ functions, and the sums to products of $_{0} F_{1}$ (Bessel) and $_{1} F_{2}$ 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.

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

Abstract

References in corpus (2)

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