A264156 Decimal expansion of M_5, the 5-dimensional analog of Madelung's constant (negated).
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
Offset: 1
Examples
-1.9093378156187685595201437984336...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.
Links
- Eric Weisstein's World of Mathematics, Madelung Constants.
Programs
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Mathematica
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
Formula
Equals (1/sqrt(Pi))*Integral_{t=0..oo} ((Sum_{k=-oo..oo} (-1)^k*exp(-k^2*t))^5 - 1)/sqrt(t) dt.