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

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, 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, 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

Offset: 2

Author

Jean-François Alcover, Aug 05 2014

Keywords

• nonn
• cons
• easy

Examples

			23.634090016154231536632674566865164174841395158861393288529...
		

Links

• M. Rogers, J. G. Wan, and I. J. Zucker, Moments of elliptic entegrals and critical L-values.
• Eric Weisstein's MathWorld, Complete Elliptic Integral of the First Kind.

Crossrefs

Cf. A068466.

Programs

Mathematica

(* NIntegrate[EllipticK[1 - x^2]^3, {x, 0, 1}] *)
RealDigits[Gamma[1/4]^8/(128*Pi^2), 10, 105] // First

PARI

intnum(x=0,1,ellK(sqrt(1-x^2))^3) \\ Charles R Greathouse IV, Feb 05 2025

PARI

gamma(1/4)^8/128/Pi^2 \\ Charles R Greathouse IV, Feb 05 2025

Formula

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