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A240965 Decimal expansion of integral_(0..1) K(1-x^2)^3 dx, where K is the complete elliptic integral of the first kind. 0

%I #8 Aug 05 2014 08:18:13

%S 2,3,6,3,4,0,9,0,0,1,6,1,5,4,2,3,1,5,3,6,6,3,2,6,7,4,5,6,6,8,6,5,1,6,

%T 4,1,7,4,8,4,1,3,9,5,1,5,8,8,6,1,3,9,3,2,8,8,5,2,9,0,5,2,6,8,0,3,8,1,

%U 9,4,8,7,8,2,6,2,0,5,9,5,9,1,2,0,8,1,5,2,0,7,9,6,6,3,0,5,8,8,1,1,6,7,5,5,5

%N Decimal expansion of integral_(0..1) K(1-x^2)^3 dx, where K is the complete elliptic integral of the first kind.

%H M. Rogers, J. G. Wan, and I. J. Zucker, <a href="http://arxiv.org/abs/1303.2259">Moments of elliptic entegrals and critical L-values</a>.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html">Complete Elliptic Integral of the First Kind</a>.

%F Gamma(1/4)^8/(128*Pi^2).

%e 23.634090016154231536632674566865164174841395158861393288529...

%t (* NIntegrate[EllipticK[1 - x^2]^3, {x, 0, 1}] *)

%t RealDigits[Gamma[1/4]^8/(128*Pi^2), 10, 105] // First

%Y Cf. A068466.

%K nonn,cons,easy

%O 2,1

%A _Jean-François Alcover_, Aug 05 2014

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