Some bounds for the complete elliptic integrals of the first and second kinds
Bai-Ni Guo, Feng Qi
TL;DR
This paper derives bounds for complete elliptic integrals of the first and second kinds using power series, Wallis' inequality, and a specific integral inequality, enhancing understanding of their properties.
Contribution
It introduces new bounds for elliptic integrals based on classical inequalities and series expansions, providing tighter estimates than previous results.
Findings
Derived new bounds for elliptic integrals
Utilized power series and classical inequalities
Improved estimates for elliptic integral values
Abstract
In the article, the complete elliptic integrals of the first and second kinds are bounded by using the power series expansions of some functions, the celebrated Wallis' inequality, and an integral inequality due to R. P. Agarwal, P. Cerone, S. S. Dragomir and F. Qi.
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