Asymptotic Expansion of n-dimensional Faxen-type Integrals

Richard Bruce Paris

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.

Keywords

Faxen's integral, asymptotic expansion, Wright function, generalised hypergeometric functions

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