Formulas for the approximation of the complete Elliptic Integrals

preprint2011arXivOpen access

Abstract

In this article we give evaluations of the two complete elliptic integrals KK and EE in the form of Ramanujans type-ππ formulas. The result is a formula for Γ(1/4)2π−3/2Γ(1/4)^2π^{-3/2} with accuracy about 120 digits per term.

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