A Natural Approximation to the Complete Elliptic Integral of the First Kind

Ling Zhu
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Ling Zhu: Department of Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Mathematics, 2022, vol. 10, issue 9, 1-8

Abstract: Let K ( r ) be the complete elliptic integral of the first kind. Then, the inequality 2 K ( r ) / π > tanh − 1 ( r ) / sin − 1 r holds for all r ∈ ( 0 , 1 ) . This conclusion does not match those in the existing literature.

Keywords: simple bound; natural approximation; the complete elliptic integral of the first kind (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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