On 07.08.2012 00:02, Kjetil brinchmann Halvorsen wrote:
The following example arises from a quation on Mathoverflow, and is
the expectation of the absolute value
of difference between two Poisson variables.
summation( abs(x-y)*exp(x+y)/(factorial(x)*factorial(y)),(x,0,oo),(y,0,oo))
which is only returned symbolically. According to some answers, this
should be expressible
using Bessel functions.
http://mathoverflow.net/questions/104008/e-x-y-where-x-and-y-are-independent-poisson-random-variable
Hm. As suggestd in the answer, we can consider the regions x > y and x <
y separately. Hence I suggest a substitution y = x + c, to get a summand of
abs(c)*exp(c+2*x)/factorial(x)/factorial(x+c).
Summing this for (x, 0, oo) and (c, 1, oo) gives 1/2 of the desired
answer. Sympy can do either summation, but in each case ends up with a
transcendental expression where we cannot do the other summation.
I.e., I'm sorry, I don't know how to get sympy to do this.
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