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Is it possible to have a constraint on variables in summation of series just similar to pattern constraint e.g.

Sum[Binomial[i + 3, 3]*Binomial[2, j], {i, 0, Infinity}, {j, 0, Infinity} ] 

with the condition that i + j = 2?

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1  
Can't you use the condition to remove the sum over j ? – b.gatessucks Oct 8 '13 at 8:04

Compare :

Sum[Binomial[i + 3, 3]*Binomial[2, j] Boole[i + j == 2], {i, 0, Infinity}, {j, 0, Infinity}]
(* 19 *)

and

pairs = Solve[{i + j == 2, i >= 0, j >= 0}, {i, j}, Integers]
(* {{i -> 0, j -> 2}, {i -> 1, j -> 1}, {i -> 2, j -> 0}} *)

Total[Binomial[i + 3, 3]*Binomial[2, j] /. pairs]
(* 19 *)
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thanks..it works.. – suruchi Oct 8 '13 at 9:15

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