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A118292
Decimal expansion of (Gamma(1/6)*Gamma(1/3))/(3*sqrt(Pi)).
8
2, 8, 0, 4, 3, 6, 4, 2, 1, 0, 6, 5, 0, 9, 0, 8, 5, 2, 2, 3, 5, 0, 0, 3, 8, 1, 5, 8, 1, 0, 0, 5, 8, 8, 2, 7, 0, 9, 2, 6, 0, 4, 4, 4, 1, 0, 8, 4, 7, 9, 7, 2, 1, 9, 2, 3, 6, 3, 9, 8, 7, 9, 7, 4, 1, 5, 2, 5, 6, 9, 5, 3, 1, 9, 6, 3, 6, 0, 6, 5, 9, 2, 1, 4, 1, 7, 0, 4, 5, 3, 2, 9, 7, 0, 0, 4, 9, 5, 6, 9, 4, 1, 1, 0, 3
OFFSET
1,1
COMMENTS
General formula: Integral_{x=0..1} (1+x^(3n))/sqrt(1-x^3) dx = G_3 * k_n = G_3*A146751(n)/A146752(n) = A118292*A146751(n)/A146752(n) where G_3 = (Gamma(1/3)^3)/(2^(1/3)*sqrt(3)*Pi) is the number in the present entry. For numerators of k_n see A146752, for denominators of k_n see A146753. - Artur Jasinski
gamma(1/6)*gamma(1/3)/(3*sqrt(Pi)) = gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi). - Harry J. Smith, May 09 2009
LINKS
Eric Weisstein's World of Mathematics, Butterfly Curve
FORMULA
Equals A073005^3 / (A002194*A002580*A000796) [see Vidunas, arXiv:math.CA/0403510]. - R. J. Mathar, Nov 30 2008
Equals 3/hypergeom([1/3, 1/6], [3/2], 1) = A290570*A005480. - Peter Bala, Mar 02 2022
EXAMPLE
2.8043642106509085223500381581005882709260444108... - Harry J. Smith, May 09 2009
MATHEMATICA
RealDigits[(Gamma[1/3]^3)/(2^(1/3) Sqrt[3] Pi), 10, 200] (* Artur Jasinski*)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 4080); x=gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi); for (n=1, 4000, d=floor(x); x=(x-d)*10; write("b118292.txt", n, " ", d)); } \\ Harry J. Smith, Jun 20 2009
CROSSREFS
Cf. A160323 (continued fraction). - Harry J. Smith, May 09 2009
Sequence in context: A021785 A136664 A086728 * A160584 A191334 A251794
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Apr 22 2006
EXTENSIONS
Edited by N. J. A. Sloane, Nov 16 2008 at the suggestion of R. J. Mathar
STATUS
approved