Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On a Finite Sum Involving Inverse Powers of Cosines

On a Finite Sum Involving Inverse Powers of Cosines 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

On a Finite Sum Involving Inverse Powers of Cosines

Kowalenko, Victor
Acta Applicandae Mathematicae , Volume 115 (2) – Apr 5, 2011
Download PDF
13 pages

Loading next page...
 
/lp/springer-journals/on-a-finite-sum-involving-inverse-powers-of-cosines-1vg7XF00z6

References (11)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media B.V.
Subject
Mathematics; Mechanics; Theoretical, Mathematical and Computational Physics; Mathematics, general; Statistical Physics, Dynamical Systems and Complexity; Computer Science, general
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-011-9612-z
Publisher site
See Article on Publisher Site

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.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Apr 5, 2011

There are no references for this article.