Varga's Constant

Author

Eric W. Weisstein
July 2, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/VargasConstant.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/VargasConstant.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Value

V6.0

V=c/.FindRoot[EllipticK[c^2]==2EllipticE[c^2],{c,.9},WorkingPrecision->110]

1/Exp[-((π EllipticK[1-c^2])/(EllipticK[c^2]))]

V7

V=First[1/Exp[-((π EllipticK[1-c^2])/(EllipticK[c^2]))]/.FindInstance[EllipticK[c^2]==2EllipticE[c^2],c]//FullSimplify]

N[V,10^3]