A030652 Continued fraction for Gamma(2/3).

1, 2, 1, 4, 1, 2, 8, 1, 1, 4, 4, 1, 6, 12, 1, 5, 1, 1, 1, 3, 2, 1, 1, 1, 18, 9, 1, 42, 1, 1, 2, 1, 1, 10, 3, 2, 4, 6, 2, 11, 1, 1, 8, 65, 9, 4, 1, 11, 2, 3, 1, 4, 3, 1, 2, 1, 2, 1, 5, 1, 1, 1, 2, 1, 14, 1, 5, 1, 6, 2, 7, 1, 29, 1, 1, 1, 3, 1, 2, 1, 26, 1, 1, 7, 13, 1, 2, 2, 8, 3, 4, 2, 2, 2

Offset: 0

Author

Paolo Dominici (pl.dm(AT)libero.it)

Keywords

• nonn
• cofr

Examples

			1.354117939426400416945288028... = 1 + 1/(2 + 1/(1 + 1/(4 + 1/(1 + ...)))). - _Harry J. Smith_, May 14 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..4999
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A030651, A073006 (decimal expansion).

Programs

Mathematica

ContinuedFraction[Gamma[2/3],100] (* Harvey P. Dale, Sep 05 2021 *)

PARI

{ allocatemem(932245000); default(realprecision, 5200); x=contfrac(gamma(2/3)); for (n=1, 5000, write("b030652.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 14 2009

Formula

Note that 3*GAMMA(1/3)*GAMMA(2/3) = 2*Pi*sqrt(3).

Extensions

Offset changed by Andrew Howroyd, Aug 03 2024