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.
Categories: math.GM