Asymptotic Expansion of n-dimensional Faxen-type Integrals

Abstract

The asymptotic expansion of n-dimensional extensions of Faxen's integral I_n(z) are derived for large complex values of the variable z. The theory relies on the asymptotics of the generalised hypergeometric , or Wright, 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.