Comment #28 on issue 1038 by [email protected]: (sin(x)*cos(x)).series(x,
0, 1000) takes forever
http://code.google.com/p/sympy/issues/detail?id=1038
More generally, suppose one wanted to compute the Nth coefficient of the
power series for f(x). If one can find a form p(x)*g(a*x^m) where p(x) is a
polynomial with deg(p) << N, g(x) is a function whose power series is known
(or easy to compute), and a and m are constants, then there is a very fast
algorithm for finding that Nth coefficient.
What SymPy is doing now for (sin(x)*cos(x)) is a quadratic algorithm in the
size of the series.
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