A New Lower Bound for Mathieu's Series


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New Zealand Journal of Mathematics

Vol. 44, (2014), Pages 75-81

Armen Bagdasaryan

Russian Academy of Sciences,

Institute for Control Sciences,

65 Profsoyuznaya,

117997 Moscow,


Department of Mathematics,

College of Engineering,

American University of the Middle East,

Kuwait City,

15453 Egaila,



Abstract In this paper, we establish a new lower bound for Mathieu's series and present a simple and short proof of the Mathieu's inequality. We also give a simple derivation of the integral form of the series.

Keywords Mathieu's series, bounds, estimate, Mathieu's inequality, integral representation.

Classification (MSC2000) Primary 26D15, 33E20; Secondary 33F05, 65D20.

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