%I #9 Nov 06 2015 03:39:23
%S 1,9,0,9,3,3,7,8,1,5,6,1,8,7,6,8,5,5,9,5,2,0,1,4,3,7,9,8,4,3,3,6
%N Decimal expansion of M_5, the 5-dimensional analog of Madelung's constant (negated).
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/MadelungConstants.html"> Madelung Constants</a>
%F M_5 = 1/sqrt(Pi) integral_{0..infinity} ((sum_{k=-infinity..infinity} ((-1)^k exp(-k^2 t))^5 - 1)/sqrt(t) dt
%e -1.9093378156187685595201437984336...
%t digits = 32; f[n_, x_] := 1/Sqrt[Pi*x]*(EllipticTheta[4, 0, Exp[-x]]^n - 1); M[5] = NIntegrate[f[5, x], {x, 0, Infinity}, WorkingPrecision -> digits + 5]; RealDigits[M[5], 10, digits] // First
%Y Cf. A088537, A085469, A090734, A247040, A261805, A264157.
%K nonn,cons,more
%O 1,2
%A _Jean-François Alcover_, Nov 06 2015