TL;DR
This paper introduces a new lower bound for Mathieu's series and offers a novel derivation of its expansions involving Riemann Zeta functions, enhancing understanding of its properties.
Contribution
It provides the first known lower bound and a new derivation of Mathieu's series expansions using Riemann Zeta functions.
Findings
Established a new lower bound for Mathieu's series
Derived new expansions in terms of Riemann Zeta functions
Improved theoretical understanding of Mathieu's series
Abstract
We establish a new lower bound for Mathieu's series and present a new derivation of its expansions in terms of Riemann Zeta functions.
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Taxonomy
TopicsMathematics and Applications · Advanced Numerical Analysis Techniques