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Please use this identifier to cite or link to this item: http://hdl.handle.net/10373/1286

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Title: The asymptotics of the mittag-leffler polynomials
Authors: Paris, Richard B.
Affiliation: University of Abertay Dundee. School of Computing & Engineering Systems
Keywords: Mittag-Leffler polynomials
Asymptotic expansion
Uniform approximation
Extreme zeros
Issue Date: 2012
Publisher: Journal of classical analysis
Type: Journal Article
Refereed: peer-reviewed
Citation: Paris, R. B. 2012. The asymptotics of the mittag-leffler polynomials. Journal of classical analysis. 1(1): pp.1–16. Available from doi:10.7153/jca-01-01
Abstract: We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z, where z is a complex variable satisfying 0 arg z 12 π . A summary of the asymptotic properties of Gn(ix) for real values of x and an approximation for its extreme zeros as n→∞ are given. When the variables are such that z/n is finite, an expansion is obtained using the method of steepest descents applied to a suitable integral representation. This expansion holds everywhere in the first quadrant of the z -plane except in the neighbourhood of the point z=in , where there is a coalescence of saddle points. Numerical results are presented to illustrate the accuracy of the various expansions.
URI: http://hdl.handle.net/10373/1286
Appears in Collections:Computing & Engineering Systems Collection

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