A241990 Decimal expansion of 'delta', a constant arising in the asymptotics of the regularized product of the Fibonacci numbers.

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, 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, 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

Offset: 0

Author

Jean-François Alcover, Aug 11 2014

Keywords

• nonn
• cons
• easy

Examples

			0.899212680785500886257698838775288182435045411706848498172656...
		

References

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

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 1.
• Adrian R. Kitson, The regularized product of the Fibonacci numbers. (2006) arXiv:math/0608187 [math.HO]

Crossrefs

Cf. A062073.

Programs

Mathematica

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

Formula

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...).