A241990 - OEIS

%I #18 Nov 09 2024 02:36:24

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

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

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

%N Decimal expansion of 'delta', a constant arising in the asymptotics of the regularized product of the Fibonacci numbers.

%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.5 Fibonacci factorials, p. 10.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 1.

%H Adrian R. Kitson, <a href="http://arxiv.org/abs/math/0608187">The regularized product of the Fibonacci numbers.</a> (2006) arXiv:math/0608187 [math.HO]

%F delta = 5^(1/4)*exp(-log(5)^2/(8*log(phi)))*c/phi^(1/12), where phi is the golden ratio and c is the Fibonacci factorial constant (c = A062073 = 1.226742...).

%e 0.899212680785500886257698838775288182435045411706848498172656...

%t c = QPochhammer[-1/GoldenRatio^2]; delta = 5^(1/4)*Exp[-Log[5]^2/(8*Log[GoldenRatio])]*c/GoldenRatio^(1/12); RealDigits[delta, 10, 103] // First

%Y Cf. A062073.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Aug 11 2014