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%I #5 Sep 05 2015 14:08:46
%S 0,3,7,0,0,7,2,1,6,5,8,2,2,9,0,3,0,3,2,0,9,9,2,3,7,8,9,4,4,8,9,1,9,3,
%T 3,0,0,7,0,0,7,3,9,8,0,6,2,1,3,2,8,4,7,3,6,3,8,5,0,5,7,3,0,5,9,7,0,9,
%U 3,6,6,0,0,7,7,3,2,8,3,1,2,8,0,6,7,1,0,1,0,7,7,6,7,7,9,4,9,3,7,6,4,9,6,1,3,2
%N Decimal expansion of H(1/2,1), a constant appearing in the asymptotic variance of the largest component of random mappings on n symbols, expressed as H(1/2,1)*n^2.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 289.
%F H(1/2,1) = (8/3) Integral_{0..infinity} (1-exp(Ei(-x)/2)) x dx - A143297^2, where A143297 is G(1/2,1), using Finch's notation.
%e 0.037007216582290303209923789448919330070073980621328473638505730597...
%t digits = 105; h1 = (8/3)*NIntegrate[(1 - Exp[ExpIntegralEi[-x]/2])*x, {x, 0, Infinity}, WorkingPrecision -> digits + 10]; h2 = 4*NIntegrate[1 - Exp[ExpIntegralEi[-x]/2], {x, 0, Infinity}, WorkingPrecision -> digits + 10]^2 ; Join[{0}, RealDigits[h1 - h2, 10, digits] // First]
%Y Cf. A143297.
%K nonn,cons,easy
%O 0,2
%A _Jean-François Alcover_, Sep 04 2015
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