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%I #16 Jan 05 2017 13:53:21
%S 3,1,8,7,5,9,0,6,0,9,8,0,3,8,6,6,2,4,8,1,1,9,7,2,1,7,2,4,7,6,2,1,2,5,
%T 4,3,2,2,5,3,5,0,7,7,4,6,9,9,6,8,2,2,8,2,9,0,2,1,4,1,8,1,5,8,1,8,8,7,
%U 8,8,4,7,0,3,8,3,9,9,7,6,8,0,8,1,6,0,2,0,4,6,3,9,3,3,8,8,2,9,1,3
%N Decimal expansion of a constant related to a certain Sobolev isoperimetric inequality.
%C Summarizing the definition: the supremum of the absolute value of a differentiable function f(x,y) is less than or equal to 0.318759... times the square root of the integral of the sum of squares of all partial derivatives of f.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 222.
%F Equals sqrt( 1/(2*Pi) * Integral_{t >= 1} 1/(sqrt(t^2 + 2)*sqrt(t^2 + 3)) dt ).
%F sqrt((F(log(3)/2*i, 3/2)*i + K(-1/2))/(2*Pi*sqrt(2))), with i = sqrt(-1), F and K being the elliptic integrals.
%e 0.31875906098038662481197217247621254322535...
%p Re(evalf(sqrt((EllipticF(I/sqrt(3), sqrt(3/2))*I + EllipticK(I/sqrt(2))) / (2*Pi*sqrt(2))), 120)); # _Vaclav Kotesovec_, Apr 22 2015
%t Sqrt[(EllipticF[Log[3]/2*I, 3/2]*I + EllipticK[-1/2])/(2*Pi*Sqrt[2])] // Re // RealDigits[#, 10, 100]& // First
%t RealDigits[Sqrt[(EllipticK[1/3] - EllipticF[ArcCot[Sqrt[2]], 1/3])/(2 Sqrt[3] Pi)], 10, 100][[1]] (* _Jan Mangaldan_, Jan 04 2017 *)
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, May 14 2014
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