login
A058655
Decimal expansion of area under the curve 1/Gamma(x) from zero to infinity.
9
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
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.
Eric Weisstein's World of Mathematics, 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
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