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