A Rational Approximation for the Complete Elliptic Integral of the Second Kind Based on Padé approximant

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发表日期：

2024年11月4日

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Xiao-Yan Ma,
Xing-Hua He,
Gen-Hong Zhong

摘要

For $r\in (0,1)$ $r \in (0, 1)$ , let ${\mathcal {E}}(r)$ $E (r)$ be the complete elliptic integral of the second kind. In this paper, the authors obtain a accuracy approximation for ${\mathcal {E}}(r)$ $E (r)$ , which improve the related inequalities satisfied by ${\mathcal {E}}(r)$ $E (r)$ .