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A247398 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.

%I A247398 #13 Feb 16 2025 08:33:23
%S A247398 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 A247398 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 A247398 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 A247398 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 A247398 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4 Golomb-Dickman Constant, p. 285.
%H A247398 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Golomb-DickmanConstant.html">Golomb-Dickman Constant</a>
%H A247398 Wikipedia, <a href="http://en.wikipedia.org/wiki/Golomb%E2%80%93Dickman_constant">Golomb-Dickman constant</a>
%F A247398 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 A247398 0.03690783006485220217710700292932764...
%p A247398 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 A247398 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 A247398 Cf. A084945.
%K A247398 nonn,cons
%O A247398 0,2
%A A247398 _Jean-François Alcover_, Sep 16 2014
%E A247398 More digits from _Vaclav Kotesovec_, Aug 12 2019