Special Value of the Hypergeometric Function 3F2 and Connection Formulae Among Asymptotic Expansions

Abstract

The value ₃F₂ (α₁, α₂, α₃ β₁, β₂ |1) of the hypergeometric function ₃F₂ (α₁, α₂, α₃ β₁, β₂ |z) generally has no known elementary expression (see [02], [A5]). It satisfies holonomic linear difference equations in α₁, α₂, α₃, β₁, β₂. In this note we determine the coefficients of associated connection formulae among all possible directions at the infinity. These are known to characterize it.