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
KEYWORD
AUTHOR
Jean-François Alcover, Sep 01 2015
STATUS
approved