A244850 - OEIS

%I #6 Jul 07 2014 11:19:59

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

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

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

%N Decimal expansion of 'c2', a constant (negated) closely related to 'c1', the Quinn-Rand-Strogatz (QRS) constant of nonlinear physics.

%H D. H. Bailey and J. M. Borwein, <a href="http://moodle.thecarma.net/jon/ontology.pdf">Experimental computation as an ontological game changer, 2014.</a> p. 21.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/QRSConstant.html">QRS Constant</a>.

%F c2 = c1 - c1^2 - 30*zeta(-1/2, c1/2)/zeta(3/2, c1/2), where zeta is the generalized Riemann zeta function.

%e -0.104685459433071176262158436583950361566306188422928659240897990324451611646...

%t digits = 101; c1 = z /. FindRoot[Zeta[1/2, z/2], {z, 1}, WorkingPrecision -> digits+5]; c2 = c1 - c1^2 - 30*Zeta[-1/2, c1/2]/Zeta[3/2, c1/2]; RealDigits[c2, 10, digits] // First

%Y Cf. A131329.

%K nonn,cons

%O 0,3

%A _Jean-François Alcover_, Jul 07 2014