|
| |
|
|
A068467
|
|
Decimal expansion of (1/4)! = Gamma(5/4).
|
|
2
| |
|
|
9, 0, 6, 4, 0, 2, 4, 7, 7, 0, 5, 5, 4, 7, 7, 0, 7, 7, 9, 8, 2, 6, 7, 1, 2, 8, 8, 9, 6, 6, 9, 1, 8, 0, 0, 0, 7, 4, 8, 7, 9, 1, 9, 2, 0, 7, 2, 0, 0, 1, 6, 3, 6, 6, 8, 5, 8, 3, 4, 4, 4, 9, 9, 8, 9, 2, 4, 7, 9, 8, 1, 0, 8, 8, 4, 6, 8, 2, 2, 8, 0, 4, 0, 4, 5, 9, 0, 0, 3, 4, 1, 8, 0, 8, 4, 6, 0, 7, 5, 0, 9, 0, 3, 6
(list; constant; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
REFERENCES
| J. M. Borwein and I. J. Zucker: Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind, IMA Journal of Numerical Analysis, vol. 12, no. 4, pp. 519-526, 1992.
Greg Martin: A product of Gamma function values at fractions with the same denominator, arXiv:0907.4384v1 [math.CA], 24-July-2009. URL: urlhttp://arxiv.org/abs/0907.4384.
Albert Nijenhuis: Small Gamma Products with Simple Values, arXiv:0907.1689v1 [math.CA], 9-July-2009. URL: urlhttp://arxiv.org/abs/0907.1689.
Raimundas Vidunas: Expressions for values of the gamma function, arXiv:math.CA/0403510, 30-March-2004. URL: urlhttp://arxiv.org/abs/math/0403510.
|
|
|
FORMULA
| 2^(3/4)*(2/E^(16*Pi) + 1)* Pi^(3/4)/(2^(13/16)/(Sqrt[2] - 1)^(1/4) + 2^(1/4) + 1) is a very good approximation (~88 digits) which becomes exact if you replace (2/E^(16*Pi) + 1) by EllipticTheta[3,0,E^-(16*Pi)]. [R. W. Gosper, Posting to Math Fun Mailing List, Dec 27 2011.]
|
|
|
EXAMPLE
| 0.906402477055477077982671288966918000748791920720...
|
|
|
CROSSREFS
| Cf. A202623.
Sequence in context: A199789 A019874 A197520 * A131223 A198213 A093766
Adjacent sequences: A068464 A068465 A068466 * A068468 A068469 A068470
|
|
|
KEYWORD
| cons,easy,nonn
|
|
|
AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 10 2002
|
|
|
EXTENSIONS
| Removed leading zero and adjusted offset R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 06 2009
Additional reference from Joerg Arndt, Dec 28 2011. Edited by N. J. A. Sloane,, Dec 28 2011.
|
| |
|
|
