Asymptotic expansion of n-dimensional Faxen-type integrals

Abstract

The asymptotic expansion of n-dimensional extensions of Faxén’s integral $I _n$(z) are derived for large complex values of the variable z. The theory relies on the asymptotics of the generalised hy- pergeometric, orWright, function. The coefficients in the exponential expansion are obtained by means of an algorithm applicable for arbitrary n. Numerical examples are given to illustrate the accuracy of the expansions. 2000 Mathematics Subject Classifications: 30E15, 33C70, 41A60, 41A63