Asymptotical Bounds for Complete Elliptic Integrals of the Second Kind

preprint2012arXivOpen access

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

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Asymptotical Bounds for Complete Elliptic Integrals of the Second Kind

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