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summation with mathematica
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106621] summation with mathematica
*From*: Tobias <tlautenschlager at googlemail.com>
*Date*: Tue, 19 Jan 2010 05:12:16 -0500 (EST)
Hello Everybody,
I want to calculate the following sum with Mathematica:
Sum[((3 - 2 j^2 + i (3 + 2 j)) j! Gamma[2 + j] Gamma[2 + k])/((3 + i)
^2 (2 + i - j) (3 + i - j) (j - k)! Gamma[4 + j + k]),{j,0,i},{i,
0,infinity}] with k >= 0
Trying only the first summation over j, Mathematica expresses the
result in terms of infinite Hypergeometric functions.
By setting k to any value [0,infinity], getting rid of all gamma
functions and faculties and applying partial fraction decomposition,
one is able to obtain a finite result (checked for k=0,1). Therefore,
I assume that the Gammafunctions cause the problem.
Does someone know how to avoid the infinite hypergeometric functions?
Tank you for your help
Tobias
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