OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Hassan Chamati and Nicholay S. Tonchev, Exact results for some Madelung type constants in the finite-size scaling theory, arXiv:cond-mat/0003235 [cond-mat.stat-mech], 2000.
Eric Weisstein's World of Mathematics, Madelung Constants
FORMULA
Equals 2*sqrt(Pi)*zeta(1/2)*(zeta(1/2, 1/4) - zeta(1/2, 3/4)).
Equals 4*Pi^(1 - 2*nu)*gamma(nu)*zeta(nu)*DirichletBeta(nu) with nu = 1/2.
EXAMPLE
-6.913039577009161107850187814269779123021008950691594327139798329827...
MAPLE
evalf(2*sqrt(Pi)*Zeta(1/2)*(Zeta(0, 1/2, 1/4)-Zeta(0, 1/2, 3/4)), 120); # Vaclav Kotesovec, May 11 2015
MATHEMATICA
RealDigits[2*Sqrt[Pi]*Zeta[1/2]*(Zeta[1/2, 1/4] - Zeta[1/2, 3/4]), 10, 104] // First
PROG
(PARI) 2*sqrt(Pi)*zeta(1/2)*(zetahurwitz(1/2, 1/4) - zetahurwitz(1/2, 3/4)) \\ Charles R Greathouse IV, Jan 31 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, May 11 2015
STATUS
approved