cp's OEIS Frontend

A118292 Decimal expansion of (Gamma(1/6)*Gamma(1/3))/(3*sqrt(Pi)).

%I A118292 #42 Aug 29 2025 11:04:11
%S A118292 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,
%T A118292 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,
%U A118292 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
%N A118292 Decimal expansion of (Gamma(1/6)*Gamma(1/3))/(3*sqrt(Pi)).
%C A118292 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_
%C A118292 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
%H A118292 Harry J. Smith, <a href="/A118292/b118292.txt">Table of n, a(n) for n = 1..4000</a>
%H A118292 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ButterflyCurve.html">Butterfly Curve</a>
%F A118292 Equals A073005^3 / (A002194*A002580*A000796) [see Vidunas, arXiv:math.CA/0403510]. - _R. J. Mathar_, Nov 30 2008
%F A118292 Equals 3/hypergeom([1/3, 1/6], [3/2], 1) = A290570*A005480. - _Peter Bala_, Mar 02 2022
%e A118292 2.8043642106509085223500381581005882709260444108....
%t A118292 RealDigits[(Gamma[1/3]^3)/(2^(1/3) Sqrt[3] Pi), 10, 200] (* _Artur Jasinski_*)
%o A118292 (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
%o A118292 (PARI) 3/hypergeom([1/3,1/6],[3/2],1) \\ _Charles R Greathouse IV_, Aug 29 2025
%Y A118292 Cf. A146752, A146753, A160323 (continued fraction).
%K A118292 nonn,cons,changed
%O A118292 1,1
%A A118292 _Eric W. Weisstein_, Apr 22 2006
%E A118292 Edited by _N. J. A. Sloane_, Nov 16 2008 at the suggestion of _R. J. Mathar_