OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
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
Albert Nijenhuis, Small Gamma Products with Simple Values, arXiv:0907.1689v1 [math.CA], 9-July-2009.
Raimundas Vidunas, Expressions for values of the gamma function, arXiv:math/0403510 [math.CA], 30-March-2004.
Wikipedia, Particular values of the Gamma function
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,exp(-(16*Pi))]. [R. W. Gosper, Posting to Math Fun Mailing List, Dec 27 2011.]
Equals A068466 /4 . - R. J. Mathar, Jan 10 2013
Also equals integral_{0..oo} exp(-x^4) dx. - Jean-François Alcover, Mar 29 2013
Equals 2^(-5/4)*Pi^(3/4)*Product_{k>=1} tanh(Pi*k/2). - Keshav Raghavan, Aug 25 2016
EXAMPLE
0.906402477055477077982671288966918000748791920720...
MAPLE
evalf(GAMMA(5/4)) ; # R. J. Mathar, Jan 10 2013
MATHEMATICA
RealDigits[Gamma[5/4], 10, 120][[1]] (* Harvey P. Dale, Aug 23 2013 *)
PROG
(PARI) gamma(5/4) \\ Altug Alkan, Sep 18 2016
(Magma) SetDefaultRealField(RealField(100)); Gamma(5/4); // G. C. Greubel, Mar 11 2018
CROSSREFS
KEYWORD
AUTHOR
Benoit Cloitre, Mar 10 2002
EXTENSIONS
Removed leading zero and adjusted offset, R. J. Mathar, Feb 06 2009
Additional reference from Joerg Arndt, Dec 28 2011
Edited by N. J. A. Sloane, Dec 28 2011
STATUS
approved