2
$\begingroup$

If we suppose that $[x^n] f(x)$ represents the coefficient of $x^n$ in a power series or generating function, I'd like to know how fast it can be calculated.

There are some restrictions that I'd like to consider, which probably change the question. The first restriction is that only basic arithmetic operations are allowed in the function (such as addition, subtraction, multiplication, and division). The second, and perhaps one that can be overlooked, is that the coefficients themselves must be integers.

The reason I'm asking this question is because I'm considering researching and writing about a technique for doing this calculation. It's fairly complicated, so I guess I almost need to write a paper on it if I want to describe it. I'd like to know if there might be a simpler or better way to do the same thing.

Additionally, I'd like to know the asymptotic bounds for the answers.

  • 0
    @GEdgar Great book!2012-03-08

0 Answers 0