A261805 Decimal expansion of M_8, the 8th Madelung constant (negated).

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

Offset

1,1

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's MathWorld, Madelung Constants

Formula

M_8 = (15/(4*Pi^3))*(8*sqrt(2) - 1)*zeta(1/2)*zeta(7/2).

Example

-2.052466827269271228176337799173383991708377529965582...

Mathematica

M8 = (15/(4*Pi^3))*(8*Sqrt[2] - 1)*Zeta[1/2]*Zeta[7/2]; RealDigits[M8, 10, 103] // First

Prog

(PARI) th4(x)=1+2*sumalt(n=1, (-1)^n*x^n^2)
intnum(x=0, [oo, 1], (th4(exp(-x))^8-1)/sqrt(Pi*x)) \\ Charles R Greathouse IV, Jun 06 2016

Crossrefs

Cf. A059750, A088537, A085469, A090734, A247040, A261804.

Sequence in context: A240663 A066283 A267213 * A300703 A300706 A351481

Adjacent sequences: A261802 A261803 A261804 * A261806 A261807 A261808

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 01 2015

Status

approved