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?

Tobias

```

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