The following series has had me held up for the past one week:

$$ \sum_{n=0}^\infty\frac{(2m)_n m^n}{(2m+1/2)_n n!}A^{3n/2} t^n K_{2m+n-1/2}(2\sqrt{A}t)~~~~ A>0, ~t>0, ~m\geq1/2 $$

where $K_{2m+n-1/2}( \cdot )$ is the Modified Bessel Function of the 2nd kind. I have looked into a number of handbooks on special functions, but to no avail.

Any ideas on how to obtain the sum?

thatsound? – J. M. Nov 26 '11 at 14:53