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Decimal expansion of the Madelung type constant C(4|1) (negated).
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%I #30 Sep 18 2021 08:11:37

%S 5,5,4,5,1,7,7,4,4,4,4,7,9,5,6,2,4,7,5,3,3,7,8,5,6,9,7,1,6,6,5,4,1,2,

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

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

%N Decimal expansion of the Madelung type constant C(4|1) (negated).

%C Without sign, this is the volume of the intersection of the three (solid) hyperboloids x^2 + y^2 - z^2 <= 1; y^2 + z^2 - x^2 <= 1; z^2 + x^2 - y^2 <= 1. See Villarino et al. - _Michel Marcus_, Aug 12 2021

%C In other words, decimal expansion of the volume of the unit trihyperboloid. - _Eric W. Weisstein_, Sep 18 2021

%H 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 Mark B. Villarino and Joseph C. Várilly, <a href="https://arxiv.org/abs/2108.05195">Archimedes' Revenge</a>, arXiv:2108.05195 [math.HO], 2021.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MadelungConstants.html">Madelung Constants</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Trihyperboloid.html">Trihyperboloid</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F -8*log(2).

%F 4*log(2)/5 = 8*log(2)/10 = Sum_{k>=1} F(k)^2/(k * 3^k), where F(k) is the k-th Fibonacci number (A000045). - _Amiram Eldar_, Aug 09 2020

%e -5.54517744447956247533785697166541254460400107488204203296544...

%p evalf(-8*log(2),120); # _Vaclav Kotesovec_, May 11 2015

%t RealDigits[-8*Log[2], 10, 103] // First

%o (PARI) -8*log(2) \\ _Charles R Greathouse IV_, Sep 02 2021

%Y Cf. A000045, A257870, A257871.

%Y Cf. A347903 (surface area of the unit trihyperboloid).

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, May 11 2015