A257872 Decimal expansion of the Madelung type constant C(4|1) (negated).

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, 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, 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

Offset: 1

Author

Jean-François Alcover, May 11 2015

Keywords

• nonn
• cons
• easy

Comments

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

In other words, decimal expansion of the volume of the unit trihyperboloid. - Eric W. Weisstein, Sep 18 2021

Examples

			-5.54517744447956247533785697166541254460400107488204203296544...
		

Links

• 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.
• Mark B. Villarino and Joseph C. Várilly, Archimedes' Revenge, arXiv:2108.05195 [math.HO], 2021.
• Eric Weisstein's World of Mathematics, Madelung Constants
• Eric Weisstein's World of Mathematics, Trihyperboloid
• Index entries for transcendental numbers

Crossrefs

Cf. A000045, A257870, A257871.

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

Programs

Maple

evalf(-8*log(2),120); # Vaclav Kotesovec, May 11 2015

Mathematica

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

PARI

-8*log(2) \\ Charles R Greathouse IV, Sep 02 2021

Formula

-8*log(2).

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