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

%I A257871 #16 Feb 16 2025 08:33:25
%S A257871 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,
%T A257871 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,
%U A257871 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
%N A257871 Decimal expansion of the Madelung type constant C(2|1/2) (negated).
%H A257871 G. C. Greubel, <a href="/A257871/b257871.txt">Table of n, a(n) for n = 1..5000</a>
%H A257871 Hassan Chamati and Nicholay S. Tonchev, <a href="http://arxiv.org/abs/cond-mat/0003235">Exact results for some Madelung type constants in the finite-size scaling theory</a>, arXiv:cond-mat/0003235 [cond-mat.stat-mech], 2000.
%H A257871 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MadelungConstants.html">Madelung Constants</a>
%F A257871 Equals 2*sqrt(Pi)*zeta(1/2)*(zeta(1/2, 1/4) - zeta(1/2, 3/4)).
%F A257871 Equals 4*Pi^(1 - 2*nu)*gamma(nu)*zeta(nu)*DirichletBeta(nu) with nu = 1/2.
%e A257871 -6.913039577009161107850187814269779123021008950691594327139798329827...
%p A257871 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
%t A257871 RealDigits[2*Sqrt[Pi]*Zeta[1/2]*(Zeta[1/2, 1/4] - Zeta[1/2, 3/4]), 10, 104] // First
%o A257871 (PARI) 2*sqrt(Pi)*zeta(1/2)*(zetahurwitz(1/2, 1/4) - zetahurwitz(1/2, 3/4)) \\ _Charles R Greathouse IV_, Jan 31 2018
%Y A257871 Cf. A257870, A257872.
%K A257871 nonn,cons,easy
%O A257871 1,1
%A A257871 _Jean-François Alcover_, May 11 2015