A073006 Decimal expansion of Gamma(2/3).

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, 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, 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

Offset: 1

Author

Robert G. Wilson v, Aug 03 2002

Keywords

• cons
• nonn

Comments

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

Examples

			1.354117939426400416945288028154513785519327266056793698394022467963782...
		

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 43, equation 43:4:8 at page 413.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..5000
• Simon Plouffe, GAMMA(2/3).
• Index to sequences related to the Gamma function.
• Index entries for transcendental numbers.

Crossrefs

Cf. A030652 (continued fraction). - Harry J. Smith, May 14 2009

Cf. A073005, A186706.

Programs

Magma

SetDefaultRealField(RealField(100)); Gamma(2/3); // G. C. Greubel, Mar 10 2018

Mathematica

RealDigits[ N[ Gamma[2/3], 110]][[1]]

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

Formula

Gamma(2/3) * A073005 = A186706. - R. J. Mathar, Jun 18 2006