OFFSET
0,1
COMMENTS
Define g(0, x) = 1/4 if -2 <= x <= 2, otherwise g(0, x) = 0; g(n, x) = Integral_{y=x - 2/(2*n+1)..x + 2/(2*n+1)} g(n - 1, y)*(2*n+1)/4 dy for n > 0. With t_i being independent random variables with common distribution P(t_i = 1) = P(t_i = -1) = 1/2, the probability of random harmonic series Sum_{i>=1} (t_i)/i converging to x is lim_{n->infinity} g(n, x).
LINKS
Byron Schmuland, Random Harmonic Series, The American Mathematical Monthly, Vol. 110, No. 5 (May, 2003), pp. 407-416.
EXAMPLE
0.249915039...
CROSSREFS
KEYWORD
AUTHOR
Jinyuan Wang, Oct 02 2020
STATUS
approved