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- Title
Some Remarks on the Mathieu Series.
- Authors
Frontczak, Robert
- Abstract
The object of this note is to present new expressions for the classical Mathieu series in terms of hyperbolic functions. The derivation is based on elementary arguments concerning the integral representation of the series. The results are used afterwards to prove, among others, a new relationship between the Mathieu series and its alternating companion. A recursion formula for the Mathieu series is also presented. As a byproduct, some closed-form evaluations of integrals involving hyperbolic functions are inferred.
- Subjects
HYPERBOLIC functions; MATHEMATICAL literature; ZETA functions; NONLINEAR differential equations; MATHEMATICAL analysis
- Publication
ISRN Applied Mathematics, 2014, p1
- ISSN
2090-5564
- Publication type
Article
- DOI
10.1155/2014/985782