Asymptotic expansion of n-dimensional Faxén-type integrals

Richard B. Paris

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    The asymptotic expansion of n-dimensional extensions of Faxén’s integral In(z) are derived for large complex values of the variable z. The theory relies on the asymptotics of the generalised hypergeometric, 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.
    Original languageEnglish
    Pages (from-to)1006-1031
    Number of pages26
    JournalEuropean Journal of Pure and Applied Mathematics
    Issue number6
    Publication statusPublished - 2010


    • Asymptotic expansion
    • Faxén's integral
    • Wright function
    • Generalised hypergeometric


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