A264157 Decimal expansion of M_7, the 7-dimensional analog of Madelung's constant (negated).

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.

Links

Table of n, a(n) for n=1..67.

Eric Weisstein's World of Mathematics, Madelung Constants.

Formula

Equals (1/sqrt(Pi))*Integral_{t=0..oo} ((Sum_{k=-oo..oo} (-1)^k*exp(-k^2*t))^7-1)/sqrt(t) dt.

Example

-2.01240598979798606439503063580430044165678065812192932878490469117330...

Mathematica

digits = 32; f[n_, x_] := 1/Sqrt[Pi*x]*(EllipticTheta[4, 0, Exp[-x]]^n - 1); M[7] = NIntegrate[f[7, x], {x, 0, Infinity}, WorkingPrecision -> digits + 5]; RealDigits[M[7], 10, digits] // First

Prog

(PARI) th4(x)=1+2*sumalt(n=1, (-1)^n*x^n^2)
intnum(x=0, [oo, 1], (th4(exp(-x))^7-1)/sqrt(Pi*x)) \\ Charles R Greathouse IV, Jun 06 2016

Crossrefs

Cf. A088537, A085469, A090734, A247040, A261805, A264156.

Sequence in context: A140531 A117316 A109189 * A361853 A144172 A227318

Adjacent sequences: A264154 A264155 A264156 * A264158 A264159 A264160

Keyword

nonn,cons,changed

Author

Jean-François Alcover, Nov 06 2015

Extensions

More terms from Charles R Greathouse IV, Jun 06 2016

Status

approved