| Author |
Comment/Response |
Vojta
|
 11/26/12 4:04pm
Hello,
I am trying to compute summation of function over multiple variables. In particular I deal with terms like
function[u_, t_] :=
Sum[D[1/t!*(e + Em*e^2)^m*
RD[0, Sqrt[(l + 1)^2 - Z^2*a^2] - 1/2 (ro + 1) + n,
Sqrt[(l + 1)^2 - Z^2*a^2] - 1/2 (ro + 1),
Sqrt[1 - Z^2*a^2] - 1, l + 2*q, e/2]*
RD[0, Sqrt[(l + 1)^2 - Z^2*a^2] - 1/2 (ro + 1) + n,
Sqrt[(l + 1)^2 - Z^2*a^2] - 1/2 (ro + 1),
Sqrt[1 - Z^2*a^2] - 1, l + 2*(p - q), e/2], {e, t}] /.
e -> 0, {m, 0, t}, {l, 0, u}, {p, 0, u - l}, {q, 0,
p}, {ro, -1, 1, 2}, {n, 1, 500}]
where Em,Z,a is constant and RD is hypergeometric function
RD[0, n_, l_, L_, p_, e_] :=
Hypergeometric2F1[1 + l - n, 3 + l + L + p, 2 + 2 l, (
2 (1 + e))/((1/(1 + L) + (1 + e)/n) n)]
Now, I would expect that for higher t the summation will take longer to compute because the function inside can be complicated due to t-th derivative. However, even for t=0 when no derivative occurs it takes much longer to compute than when I explicitly define the function being summed as
RD[0, Sqrt[(l + 1)^2 - Z^2*a^2] - 1/2 (ro + 1) + n,
Sqrt[(l + 1)^2 - Z^2*a^2] - 1/2 (ro + 1), Sqrt[1 - Z^2*a^2] - 1,
l + 2*q, 0]*
RD[0, Sqrt[(l + 1)^2 - Z^2*a^2] - 1/2 (ro + 1) + n,
Sqrt[(l + 1)^2 - Z^2*a^2] - 1/2 (ro + 1), Sqrt[1 - Z^2*a^2] - 1,
l + 2*(p - q), 0]
which is just the function used earlier for particular choice of t=0. Why is the first approach so slow?
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