Some Remarks on the Mathieu Series | Zendy

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Some Remarks on the Mathieu Series

Author(s) -

Robert Frontczak

Publication year - 2014

Publication title -

isrn applied mathematics

Language(s) - English

Resource type - Journals

eISSN - 2090-5572

pISSN - 2090-5564

DOI - 10.1155/2014/985782

Subject(s) - series (stratigraphy) , recursion (computer science) , mathematics , representation (politics) , mathieu function , alternating series , pure mathematics , algebra over a field , calculus (dental) , mathematical analysis , power series , algorithm , medicine , paleontology , dentistry , politics , political science , law , biology

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.

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