The discrete analogue of Laplace’s method

Richard B. Paris

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We give a justification of the discrete analogue of Laplace’s method applied to the asymptotic estimation of sums consisting of positive terms. The case considered is the series related to the hypergeometric function pFq−1(x) (with q≥p+1) as x→+∞ discussed by Stokes [G.G. Stokes, Note on the determination of arbitrary constants which appear as multipliers of semi-convergent series, Proc. Camb. Phil. Soc. 6 (1889) 362–366]. Two examples are given in which it is shown how higher order terms in the asymptotic expansion may be derived by this procedure.
Original languageEnglish
Pages (from-to)3024-3034
Number of pages11
JournalComputers & Mathematics with Applications
Issue number19
Publication statusPublished - May 2011

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