Asymptotic expansion of n-dimensional Faxén-type integrals

Richard B. Paris

Research output: Contribution to journalArticle

Abstract

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
Volume3
Issue number6
StatePublished - 2010

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Asymptotic expansion
n-dimensional
Generalized hypergeometric function
Numerical examples
Arbitrary
Coefficient

Cite this

Paris, Richard B. / Asymptotic expansion of n-dimensional Faxén-type integrals.

In: European Journal of Pure and Applied Mathematics, Vol. 3, No. 6, 2010, p. 1006-1031.

Research output: Contribution to journalArticle

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Asymptotic expansion of n-dimensional Faxén-type integrals. / Paris, Richard B.

In: European Journal of Pure and Applied Mathematics, Vol. 3, No. 6, 2010, p. 1006-1031.

Research output: Contribution to journalArticle

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AU - Paris,Richard B.

PY - 2010

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AB - 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.

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EP - 1031

JO - European Journal of Pure and Applied Mathematics

T2 - European Journal of Pure and Applied Mathematics

JF - European Journal of Pure and Applied Mathematics

SN - 1307-5543

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