Asymptotic expansions of the Lauricella hypergeometric function \(F _{D}\) (Q1872983)

The authors presented an integral representation of the Lauricella hypergeometric function in the form of a generalized Stieltjes transform. Distributional approach is applied to the integral to derive four asymptotic expansions of the function. The authors also determined the error bounds for the remainder of the asymptotic expansions at any order of the approximation. The bounds were shown considerably accurate by means of numerical experiments.