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

Kjetil

-- 
"If you want a picture of the future - imagine a boot stamping on the
human face - forever."

George Orwell (1984)

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