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

0,1

References

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

Links

Table of n, a(n) for n=0..102.

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]

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...).

Example

0.899212680785500886257698838775288182435045411706848498172656...

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

Crossrefs

Cf. A062073.

Sequence in context: A244959 A377999 A345987 * A358519 A256923 A347219

Adjacent sequences: A241987 A241988 A241989 * A241991 A241992 A241993

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 11 2014

Status

approved