I've read that the way we compute power series these days is not how it was originally done. These days, we compute the derivatives of the function we wish to expand in order to compute the power series. I've heard that this is backwards from the historical development, where one would compute the power series in order to know the derivatives.
How does this work? I believe it has something to do with some sort of iterative method of interpolating polynomials, but I'm not so sure actually. Thank you!