OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.6 Fransén-Robinson constant, p. 262.
LINKS
Steven R. Finch Errata and Addenda to Mathematical Constants p. 35.
Eric Weisstein's MathWorld Fransén-Robinson Constant
Wikipedia, Reciprocal gamma function
FORMULA
(1/I)*Integral_{x>=0} x^2/gamma(x) dx where I = Integral_{x>=0} 1/gamma(x) dx is the Fransén-Robinson constant.
EXAMPLE
4.83648597463342689473636069232113892436851608107360722903294224216...
MATHEMATICA
digits = 101;
I0 = NIntegrate[1/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];
M2 = (1/I0) NIntegrate[x^2/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];
RealDigits[M2, 10, digits][[1]]
PROG
(PARI) default(realprecision, 120); intnum(x=0, [[1], 1], x^2/gamma(x))/intnum(x=0, [[1], 1], 1/gamma(x)) \\ Vaclav Kotesovec, May 14 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, May 14 2016
STATUS
approved