A046943 Continued fraction for Fransen-Robinson constant Integral_{x>=0} 1/Gamma(x).

2, 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 10, 1, 4, 7, 2, 2, 2, 46, 18, 1, 1, 3, 1, 1, 4, 5, 1, 1, 28, 6, 2, 1, 23, 1, 6, 1, 18, 1, 4, 1, 2, 1, 3, 2, 3, 5, 1, 1, 7, 1, 1, 1, 8, 1, 1, 1, 1, 2, 1, 7, 2, 2, 1, 1, 1, 1, 6, 1, 2, 2, 11, 2, 1, 1, 3, 7, 1

Offset: 0

Author

Wouter Meeussen

Keywords

• cofr
• nonn

Examples

			2.807770242028519365221501186... = 2 + 1/(1 + 1/(4 + 1/(4 + 1/(1 + ...)))).
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1033
• A. Fransen, Accurate Determination of the Inverse Gamma Integral, Nordisk Tidskr. Informationsbehandling (BIT) 19, 137-138, 1979.
• A. Fransen and S. Wrigge, High-Precision Values of the Gamma Function and of Some Related Coefficients, Math. Comput. 34, 553-566, 1980.
• A. Fransen and S. Wrigge, Addendum and Corrigendum to 'High-Precision Values of the Gamma Function and of Some Related Coefficients' Math. Comput. 37, 233-235, 1981.
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A058655 (decimal expansion). - Harry J. Smith, May 13 2009

Programs

Mathematica

f := N[Integrate[1/Gamma[x], {x, 0, Infinity}], 55]; ContinuedFraction[f, 50] (* G. C. Greubel, Nov 06 2017 *)