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
Examples
2.807770242028519365221501186557772932308085920930198291220054809597100...
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.
Crossrefs
Cf. A046943 (continued fraction).
Programs
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Mathematica
RealDigits[ NIntegrate[ 1 / Gamma[ x ], {x, 0, Infinity}, AccuracyGoal -> 72, WorkingPrecision -> 90 ] ][ [ 1 ] ] -
PARI
intnum(x=0,[[1],1],1/gamma(x)) \\ Bill Allombert, May 18 2015
Formula
Equals e + Integral_{x=0..oo} exp(-x)/(Pi^2 + log(x)^2) dx. - Amiram Eldar, Aug 13 2020
Extensions
More terms from Philip Sung (philip_sung(AT)hotmail.com), Jan 22 2002
Comments