|
| |
|
|
A097669
|
|
Decimal expansion of the constant 5*exp(psi(3/5)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620).
|
|
2
| |
|
|
1, 9, 0, 7, 9, 5, 9, 5, 3, 2, 5, 4, 3, 5, 4, 2, 5, 2, 2, 5, 5, 3, 3, 3, 8, 1, 3, 9, 7, 2, 9, 5, 2, 0, 3, 6, 9, 0, 8, 5, 1, 6, 0, 6, 8, 3, 5, 9, 0, 8, 2, 9, 6, 8, 2, 2, 8, 2, 2, 3, 5, 9, 6, 0, 8, 1, 0, 7, 0, 6, 3, 7, 8, 6, 8, 8, 6, 5, 5, 0, 4, 0, 3, 9, 9, 7, 2, 3, 6, 3, 5, 8, 3, 0, 9, 0, 1, 3, 8, 0, 7, 5, 3, 9, 0
(list; constant; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| This constant appears in Benoit Cloitre's generalized Euler-Gauss formula for the Gamma function (see Cloitre link) and is involved in the exact determination of asymptotic limits of certain order-5 linear recursions with varying coefficients (see A097680 for example).
|
|
|
REFERENCES
| A. M. Odlyzko, Linear recurrences with varying coefficients, in Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grotschel and L. Lovasz, eds., Elsevier, Amsterdam, 1995, pp. 1135-1138.
|
|
|
LINKS
| Benoit Cloitre, On a generalization of Euler-Gauss formula for the Gamma function, pre-print 2004.
Xavier Gourdon and Pascal Sebah, Introduction to the Gamma Function.
Andrew Odlyzko, Asymptotic enumeration methods, in Handbook of Combinatorics, vol. 2, 1995, pp. 1063-1229.
|
|
|
FORMULA
| c = ((sqrt(5)+1)/2)^(sqrt(5)/2)/5^(1/4)*exp(Pi/2*sqrt(1-2/sqrt(5)))
|
|
|
EXAMPLE
| c = 1.90795953254354252255333813972952036908516068359082968228223...
|
|
|
MATHEMATICA
| RealDigits[ GoldenRatio^(Sqrt[5]/2)/5^(1/4)*E^(Pi/2Sqrt[1 - 2/Sqrt[5]]), 10, 105][[1]] (from Robert G. Wilson v Aug 27 2004)
|
|
|
PROG
| (PARI) 5*exp(psi(3/5)+Euler)
|
|
|
CROSSREFS
| Cf. A097663-A097668, A097670-A097676.
Sequence in context: A196549 A173164 A181446 * A202955 A019820 A019985
Adjacent sequences: A097666 A097667 A097668 * A097670 A097671 A097672
|
|
|
KEYWORD
| cons,nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2004
|
|
|
EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 27 2004
|
| |
|
|
