A118292 - OEIS

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A118292

Decimal expansion of (Gamma(1/6)*Gamma(1/3))/(3*sqrt(Pi)).

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

(list; constant; graph; refs; listen; history; text; internal format)

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

Harry J. Smith, Table of n, a(n) for n = 1..4000

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. A146752, A146753

Cf. A160323 (continued fraction). - Harry J. Smith, May 09 2009

Sequence in context: A021785 A136664 A086728 * A160584 A191334 A251794

Adjacent sequences: A118289 A118290 A118291 * A118293 A118294 A118295

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