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

%I A058655 #37 Feb 16 2025 08:32:43
%S A058655 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,
%T A058655 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,
%U A058655 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
%N A058655 Decimal expansion of area under the curve 1/Gamma(x) from zero to infinity.
%C A058655 Referred to as the Fransén-Robinson constant.
%C A058655 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
%D A058655 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See pp. 262-264.
%H A058655 Harry J. Smith, <a href="/A058655/b058655.txt">Table of n, a(n) for n = 1..1001</a>
%H A058655 Arne Fransén, <a href="https://doi.org/10.1007/BF01931232">Accurate determination of the inverse gamma integral</a>, BIT Numerical Mathematics, Vol. 19, No. 1 (1979), pp. 137-138.
%H A058655 Arne Fransén, <a href="https://doi.org/10.1090/S0025-5718-1981-0616377-4">Addendum and Corrigendum to "High-Precision Values of the Gamma Function and of Some Related Coefficients"'</a>, Mathematics of Computation, Vol. 37, No. 155 (1981), pp. 233-235.
%H A058655 Arne Fransén and Staffan Wrigge, <a href="https://doi.org/10.1090/S0025-5718-1980-0559204-5">High-precision values of the gamma function and of some related coefficients</a>, Mathematics of Computation, Vol. 34, No. 150 (1980), pp. 553-566.
%H A058655 F. Johansson, <a href="http://www.fredrikj.net/math/fransen_robinson.txt">Value to 1000 decimal places</a>.
%H A058655 Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/fransen.txt">Fransen-Robinson constant</a>.
%H A058655 Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap34.html">Fransen-Robinson constant</a>.
%H A058655 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fransen-RobinsonConstant.html">Fransén-Robinson Constant</a>.
%H A058655 Wikipedia, <a href="https://en.wikipedia.org/wiki/Frans%C3%A9n%E2%80%93Robinson_constant">Fransén-Robinson constant</a>.
%F A058655 Equals e + Integral_{x=0..oo} exp(-x)/(Pi^2 + log(x)^2) dx. - _Amiram Eldar_, Aug 13 2020
%e A058655 2.807770242028519365221501186557772932308085920930198291220054809597100...
%t A058655 RealDigits[ NIntegrate[ 1 / Gamma[ x ], {x, 0, Infinity}, AccuracyGoal -> 72, WorkingPrecision -> 90 ] ][ [ 1 ] ]
%o A058655 (PARI) intnum(x=0,[[1],1],1/gamma(x)) \\ Bill Allombert, May 18 2015
%Y A058655 Cf. A046943 (continued fraction).
%K A058655 nonn,cons
%O A058655 1,1
%A A058655 _Robert G. Wilson v_, Jan 05 2001
%E A058655 More terms from Philip Sung (philip_sung(AT)hotmail.com), Jan 22 2002