A030651 Continued fraction for Gamma(1/3).

2, 1, 2, 8, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 9, 1, 4, 1, 3, 1, 7, 1, 1, 3, 6, 2, 2, 1, 1, 32, 3, 3, 3, 1, 24, 2, 2, 25, 1, 2, 1, 6, 2, 1, 1, 3, 1, 9, 3, 2, 1, 6, 7, 2, 8, 2, 5, 1, 5, 1, 2, 2, 2, 2, 4, 3, 1, 5, 1, 15, 1, 1, 2, 4, 3, 3, 1, 5, 1, 4, 1, 8, 1, 3, 1, 1, 8, 2, 1, 2, 1, 514, 1, 2, 1, 1, 1

Offset: 0

Author

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

Keywords

• nonn
• cofr

Examples

			Gamma(1/3) = 2.67893853470774... = 2 + 1/(1 + 1/(2 + 1/(8 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 20 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..999
• Gang Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A030652, A073005 (decimal expansion).

Programs

Mathematica

ContinuedFraction[Gamma[1/3], 50] (* Alonso del Arte, Mar 30 2020 *)

PARI

{ default(realprecision, 1080); x=contfrac(gamma(1/3)); for (n=1, 1000, write("b030651.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 20 2009

Formula

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

Extensions

Offset changed by Andrew Howroyd, Aug 03 2024