# Question:Slow series summation

## Question:Slow series summation

Hello, I trying to sum up a series which involves several binomial terms, Maple simply gets stuck and give no results. I think I am not being smart to improve Maple performance. Please, see my code below:

>n1 := 423; x := 16; n2 := 81; y := 35; s1 := 0.1; b1 := 7; beta1 := 2.1; s2 := 0.1; b2 := 7; beta2 := 2.1;

>A := (h, v) -> Sum(Sum(binomial(n1 - x, j)*binomial(n2 - y, l)*(-1)^(j + l)*GAMMA(s1 + h + 1)*GAMMA(s2 + v + 1)*(-1)^(h + v)*(beta1 - 1)^h*(beta2 - 1)^v/(h!*GAMMA(s1 + 1)*v!*GAMMA(s2 + 1)*(x + b1*s1 + j + b1*h + y + b2*s2 + l + b2*v)*(r + x + b1*s1 + j + b1*v)), j = 0 .. n1 - x), l = 0 .. n2 - y);

>B := (h, v) -> Sum(Sum(binomial(n1 - x, j)*binomial(n2 - y, l)*(-1)^(j + l)*GAMMA(s1 + v + 1)*GAMMA(s2 + h + 1)*(-1)^(h + v)*(beta1 - 1)^v*(beta2 - 1)^h/(v!*GAMMA(s1 + 1)*h!*GAMMA(s2 + 1)*(y + b2*s2 + l + b2*h + x + b1*s1 + j + b1*v)*(y + b2*s2 + l + b2*h - r)), j = 0 .. n1 - x), l = 0 .. n2 - y)

>f := (r, upto) -> sum(sum(A(h, v) + B(h, v), v = 0 .. upto), h = 0 .. upto);

>f(0,30);

Summing up to 30 is very slow, I have left it running over many hours and no result was provided. Could we improve the way it is summing up? thanks in advance.

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