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 A068467 Decimal expansion of (1/4)! = Gamma(5/4). 8
 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; text; internal format)
 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 Cf. A202623. Sequence in context: A199789 A019874 A197520 * A131223 A225464 A296566 Adjacent sequences:  A068464 A068465 A068466 * A068468 A068469 A068470 KEYWORD cons,easy,nonn 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

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)