Asymptotical Bounds for Complete Elliptic Integrals of the Second Kind

Published 1 Sep 2012 in math.CA and math.CV | (1209.0066v1)

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 $\mathcal{E}(r)>\pi[(1+(1-r^{2)^{{3/4})/2]^{2/3}/2$}} for all $r\in(0,1)$ proposed by M. Vuorinen.

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