Unit-shift in arguments of transformed generalized hypergeometric functions: The case of 4F3(β, −1/2 , 1, 3/2; β+σ, 1/2 , 3; z)

Abstract

The function ₄F₃(β, −1/2 , 1, 3/2 ; β+σ, 1/2, 3; z) is shown to have a transformation equation in terms of ₂F₁(1−z), which is a unit-shift in argument. Subsequently, a new closed form expression for the ₄F₃ at unit argument is found.