Asymptotical Bounds for Complete Elliptic Integrals of the Second Kind

2012/09/01 by Miao-Kun Wang, Yu‐Ming Chu, Wang, Miao-Kun +1
Mathematics · #33E05 #Advanced Harmonic Analysis Research #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #G.1.2 #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1209.0066

openalex publication_date 2012/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish several asymptotical bounds for the complete elliptic integrals of the second kind E(r), and improve the well-known conjecture E(r)>π[(1+(1-r²)^3/4)/2]^2/3/2 for all r∈(0,1) proposed by M. Vuorinen.

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