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Title: The discrete analogue of Laplace’s method
Authors: Paris, Richard B.
Affiliation: University of Abertay Dundee. School of Computing & Engineering Systems
Keywords: Laplace’s method
Sums
Asymptotic expansion
Issue Date: May-2011
Publisher: Elsevier
Type: Journal Article
Refereed: peer-reviewed
Rights: This is the author's final version of this article. Published version (c)Elsevier, available from http://dx.doi.org/10.1016/j.camwa.2011.03.092
Citation: Paris, R.B. The discrete analogue of Laplace’s method. Computers & Mathematics with Applications. 61(10): pp.3024-3034. Available from http://dx.doi.org/10.1016/j.camwa.2011.03.092
Abstract: 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.
URI: http://hdl.handle.net/10373/1030
ISSN: 0898-1221
Appears in Collections:Computing & Engineering Systems Collection

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