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Decimal expansion of the smallest positive root of the function lambda(x) = sum_{n=0..infinity} (-1)^n*x^n/(2^(n*(n-1)/2)*n!).
1

%I #7 Jul 28 2014 13:00:47

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

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

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

%N Decimal expansion of the smallest positive root of the function lambda(x) = sum_{n=0..infinity} (-1)^n*x^n/(2^(n*(n-1)/2)*n!).

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 310.

%e 1.48807854559971029465624603158235766189351615260299080774972682501250548...

%t digits = 103; lambda[x_?NumericQ] := NSum[(-1)^n*x^n/(2^(n*(n - 1)/2)*n!), {n, 0, Infinity}, WorkingPrecision -> digits + 10, Method -> "AlternatingSigns"]; xi = x /. FindRoot[lambda[x] == 0, {x, 3/2}, WorkingPrecision -> digits + 10]; RealDigits[xi, 10, digits] // First

%Y Cf. A003024.

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, Jul 28 2014