%I #32 Aug 21 2023 12:01:16
%S 1,3,5,4,1,1,7,9,3,9,4,2,6,4,0,0,4,1,6,9,4,5,2,8,8,0,2,8,1,5,4,5,1,3,
%T 7,8,5,5,1,9,3,2,7,2,6,6,0,5,6,7,9,3,6,9,8,3,9,4,0,2,2,4,6,7,9,6,3,7,
%U 8,2,9,6,5,4,0,1,7,4,2,5,4,1,6,7,5,8,3,4,1,4,7,9,5,2,9,7,2,9,1,1,1,0,6,4,3
%N Decimal expansion of Gamma(2/3).
%C This constant is transcendental: Chudnovsky famously proved that Gamma(1/3) is algebraically independent of Pi, but Gamma(1/3)*Gamma(2/3) = 2*Pi/sqrt(3) by the reflection formula. - _Charles R Greathouse IV_, Aug 21 2023
%H Harry J. Smith, <a href="/A073006/b073006.txt">Table of n, a(n) for n = 1..5000</a>
%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap39.html">GAMMA(2/3)</a>
%H <a href="/index/Ga#gamma_function">Index to sequences related to the Gamma function</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F This number * A073005 = A186706. - _R. J. Mathar_, Jun 18 2006
%e 1.354117939426400416945288028154513785519327266056793698394022467963782...
%t RealDigits[ N[ Gamma[2/3], 110]][[1]]
%o (PARI) allocatemem(932245000); default(realprecision, 5080); x=gamma(2/3); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b073006.txt", n, " ", d)); \\ _Harry J. Smith_, May 14 2009
%o (Magma) SetDefaultRealField(RealField(100)); Gamma(2/3); // _G. C. Greubel_, Mar 10 2018
%Y Cf. A030652 (continued fraction). - _Harry J. Smith_, May 14 2009
%Y Cf. A073005, A186706.
%K cons,nonn
%O 1,2
%A _Robert G. Wilson v_, Aug 03 2002