A257871 Decimal expansion of the Madelung type constant C(2|1/2) (negated).

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

Offset: 1

Author

Jean-François Alcover, May 11 2015

Keywords

• nonn
• cons
• easy

Examples

			-6.913039577009161107850187814269779123021008950691594327139798329827...
		

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

Crossrefs

Cf. A257870, A257872.

Programs

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

PARI

2*sqrt(Pi)*zeta(1/2)*(zetahurwitz(1/2, 1/4) - zetahurwitz(1/2, 3/4)) \\ Charles R Greathouse IV, Jan 31 2018

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.