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A264157 Decimal expansion of M_7, the 7-dimensional analog of Madelung's constant (negated). 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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 MathWorld, Madelung Constants

FORMULA

M_7 = 1/sqrt(Pi) integral_{0..infinity} ((sum_{k=-infinity..infinity} ((-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, A264157.

Sequence in context: A140531 A117316 A109189 * A144172 A227318 A166692

Adjacent sequences:  A264154 A264155 A264156 * A264158 A264159 A264160

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Nov 06 2015

EXTENSIONS

More terms from Charles R Greathouse IV, Jun 06 2016

STATUS

approved

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Last modified March 1 03:09 EST 2021. Contains 341732 sequences. (Running on oeis4.)