A058655 Decimal expansion of area under the curve 1/Gamma(x) from zero to infinity.

2, 8, 0, 7, 7, 7, 0, 2, 4, 2, 0, 2, 8, 5, 1, 9, 3, 6, 5, 2, 2, 1, 5, 0, 1, 1, 8, 6, 5, 5, 7, 7, 7, 2, 9, 3, 2, 3, 0, 8, 0, 8, 5, 9, 2, 0, 9, 3, 0, 1, 9, 8, 2, 9, 1, 2, 2, 0, 0, 5, 4, 8, 0, 9, 5, 9, 7, 1, 0, 0, 8, 8, 9, 1, 2, 1, 9, 0, 1, 6, 6, 5, 5, 1, 0, 1, 8, 5, 3, 0, 8, 1, 6, 8, 1, 9, 6, 6, 3, 8, 1, 4, 1, 8, 7

Offset

1,1

Comments

Referred to as the Fransén-Robinson constant.

Named Fransén-Robinson constant after Herman P. Robinson, who calculated its value to 36 decimal digits (Fransén, 1979), and Arne Fransén, who calculated its value to 80 decimal digits (1981). - Amiram Eldar, Aug 13 2020

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See pp. 262-264.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1001

Arne Fransén, Accurate determination of the inverse gamma integral, BIT Numerical Mathematics, Vol. 19, No. 1 (1979), pp. 137-138.

Arne Fransén, Addendum and Corrigendum to "High-Precision Values of the Gamma Function and of Some Related Coefficients"', Mathematics of Computation, Vol. 37, No. 155 (1981), pp. 233-235.

Arne Fransén and Staffan Wrigge, High-precision values of the gamma function and of some related coefficients, Mathematics of Computation, Vol. 34, No. 150 (1980), pp. 553-566.

F. Johansson, Value to 1000 decimal places.

Simon Plouffe, Fransen-Robinson constant.

Simon Plouffe, Fransen-Robinson constant.

Eric Weisstein's World of Mathematics, Fransén-Robinson Constant.

Wikipedia, Fransén-Robinson constant.

Formula

Equals e + Integral_{x=0..oo} exp(-x)/(Pi^2 + log(x)^2) dx. - Amiram Eldar, Aug 13 2020

Example

2.807770242028519365221501186557772932308085920930198291220054809597100...

Mathematica

RealDigits[ NIntegrate[ 1 / Gamma[ x ], {x, 0, Infinity}, AccuracyGoal -> 72, WorkingPrecision -> 90 ] ][ [ 1 ] ]

Prog

(PARI) intnum(x=0, [[1], 1], 1/gamma(x)) \\ Bill Allombert, May 18 2015

Crossrefs

Cf. A046943 (continued fraction).

Sequence in context: A309420 A246725 A188934 * A058964 A021360 A028256

Adjacent sequences: A058652 A058653 A058654 * A058656 A058657 A058658

Keyword

nonn,cons

Author

Robert G. Wilson v, Jan 05 2001

Extensions

More terms from Philip Sung (philip_sung(AT)hotmail.com), Jan 22 2002

Status

approved