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

Author

Jean-François Alcover, Sep 01 2015

Keywords

• nonn
• cons
• easy

Examples

			-2.052466827269271228176337799173383991708377529965582...
		

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

Crossrefs

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

Programs

Mathematica

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

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

Formula

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