A247398 - OEIS

%I #12 Aug 12 2019 10:30:35

%S 0,3,6,9,0,7,8,3,0,0,6,4,8,5,2,2,0,2,1,7,7,1,0,7,0,0,2,9,2,9,3,2,7,6,

%T 4,0,2,2,4,6,2,2,3,3,1,0,5,8,6,8,5,1,9,6,4,7,6,2,2,7,8,2,0,7,3,0,4,8,

%U 9,1,9,4,7,1,5,3,0,8,0,6,2,8,5,1,1,8,9,3,0,4,4,9,1,0,3,4,3

%N Decimal expansion of a constant 'v' such that the asymptotic variance of the distribution of the longest cycle given a random n-permutation evaluates as v*n^2.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4 Golomb-Dickman Constant, p. 285.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Golomb-DickmanConstant.html">Golomb-Dickman Constant</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Golomb%E2%80%93Dickman_constant">Golomb-Dickman constant</a>

%F v = integral_{0..infinity} x-e^Ei(-x)*x dx - (integral_{0..infinity} 1-e^Ei(-x) dx)^2, where Ei is the exponential integral function. [corrected by _Vaclav Kotesovec_, Aug 12 2019]

%e 0.03690783006485220217710700292932764...

%p evalf(int((x-exp(Ei(-x))*x),x=0..infinity) - int( (1-exp(Ei(-x))),x=0..infinity)^2, 50); # _Vaclav Kotesovec_, Aug 12 2019

%t v = NIntegrate[x - E^ExpIntegralEi[-x]*x, {x, 0, Infinity}, WorkingPrecision -> 80] - NIntegrate[1 - E^ExpIntegralEi[-x], {x, 0, Infinity}, WorkingPrecision -> 80]^2; Join[{0}, RealDigits[v, 10, 40] // First]

%Y Cf. A084945.

%K nonn,cons

%O 0,2

%A _Jean-François Alcover_, Sep 16 2014

%E More digits from _Vaclav Kotesovec_, Aug 12 2019