The asymptotics of a new exponential sum

Authors:
R. B. Paris
Affiliations:
Division of Complex Systems, University of Abertay Dundee, Dundee DD1 1HG, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

The absolutely convergent exponential sum S"p(@q;m)=@?n=0~^'exp(-n/m-i@qe^-^p^n^/^m)@q0,p0 is studied for m-+~ and fixed p when the parameter @q is allowed to become large such that @q/m remains finite. This situation corresponds, in general, to the trace in the complex plane of the partial sums of S"p(@q;m) consisting of a multiple spiral structure. Numerical results are presented to illustrate the accuracy of the expansion.