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Decimal expansion of M_7, the 7-dimensional analog of Madelung's constant (negated).
2

%I #14 Mar 04 2023 10:05:17

%S 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,

%T 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

%N Decimal expansion of M_7, the 7-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 World of Mathematics, <a href="http://mathworld.wolfram.com/MadelungConstants.html">Madelung Constants</a>.

%F M_7 = 1/sqrt(Pi) integral_{0..infinity} ((sum_{k=-infinity..infinity} ((-1)^k exp(-k^2 t))^7-1)/sqrt(t) dt

%e -2.01240598979798606439503063580430044165678065812192932878490469117330...

%t 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

%o (PARI) th4(x)=1+2*sumalt(n=1,(-1)^n*x^n^2)

%o intnum(x=0,[oo,1], (th4(exp(-x))^7-1)/sqrt(Pi*x)) \\ _Charles R Greathouse IV_, Jun 06 2016

%Y Cf. A088537, A085469, A090734, A247040, A261805, A264157.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Nov 06 2015

%E More terms from _Charles R Greathouse IV_, Jun 06 2016