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A058655 Decimal expansion of area under the curve 1/Gamma(x) from zero to infinity. 9

%I #33 Feb 21 2023 20:11:01

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

%C Referred to as the Fransén-Robinson constant.

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

%H Harry J. Smith, <a href="/A058655/b058655.txt">Table of n, a(n) for n = 1..1001</a>

%H 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 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 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 F. Johansson, <a href="http://www.fredrikj.net/math/fransen_robinson.txt">Value to 1000 decimal places</a>.

%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/fransen.txt">Fransen-Robinson constant</a>

%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap34.html">Fransen-Robinson constant</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fransen-RobinsonConstant.html">Fransén-Robinson Constant</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Frans%C3%A9n%E2%80%93Robinson_constant">Fransén-Robinson constant</a>.

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

%e 2.807770242028519365221501186557772932308085920930198291220054809597100...

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

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

%Y Cf. A046943 (continued fraction).

%K nonn,cons

%O 1,1

%A _Robert G. Wilson v_, Jan 05 2001

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

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)