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On a Finite Sum Involving Inverse Powers of Cosines

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Abstract

A finite sum S m,v involving inverse powers of cosines has been studied previously by Fisher, who was able to solve the v=1 and v=2 cases exactly and provide the first term of an “asymptotic solution”. The series is re-visited here by using a completely different approach from Fisher’s generating function method. Higher order terms in decreasing powers of m 2 are evaluated in the large m limit. In addition, the exact calculations for the first three integer values of v are presented. An empirical method is then devised, which yields the exact formulae for all the coefficients in S m,v when v is an integer. Consequently, the first ten values of S m,v are tabulated.

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  1. ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria, 3010, Australia

    Victor Kowalenko

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  1. Victor Kowalenko
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Correspondence to Victor Kowalenko.

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Kowalenko, V. On a Finite Sum Involving Inverse Powers of Cosines. Acta Appl Math 115, 139–151 (2011). https://doi.org/10.1007/s10440-011-9612-z

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  • DOI: https://doi.org/10.1007/s10440-011-9612-z

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