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Asymptotical Bounds for Complete Elliptic Integrals of the Second Kind (1209.0066v1)
Published 1 Sep 2012 in math.CA and math.CV
Abstract: 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 $\mathcal{E}(r)>\pi[(1+(1-r2){3/4})/2]{2/3}/2$ for all $r\in(0,1)$ proposed by M. Vuorinen.