Continued fraction expression of the Mathieu series
Xiaodong Cao, Yoshio Tanigawa, Wenguang Zhai
TL;DR
This paper derives a continued fraction representation of the Mathieu series using Ramanujan's continued fraction formula, leading to new bounds for the series.
Contribution
It introduces a novel continued fraction expression for Mathieu series based on Ramanujan's formula, providing new bounds.
Findings
New continued fraction formula for Mathieu series
Improved bounds for Mathieu series
Application of Ramanujan's continued fraction in series analysis
Abstract
In this paper, we represent a continued fraction expression of Mathieu series by a continued fraction formula of Ramanujan. As application, we obtain some new bounds for Mathieu series.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Mathematical Inequalities and Applications