If p = 1+ x + O(x^2) is a power series, then then the method p.pade(0,1) should give p.pade(0,1) = 1/(1-x) but instead it gives an error
ValueError: the precision of the series is not large enough
The documentation says that p should be given up through O(x^(m+n+1)).
Isn't this wrong? Shouldn't it be up through O(x^(m+n)) ?
The Padé approximant P_m(x)/Q_n(x) contains m+n+1 unknown coefficients, so m+n+1 terms should be included in the power series: x^0 ... x^(m+n).
I'm working with a power series that I generate numerically, term by term. I'm using the pade method to estimate the region of analyticity in order to make a conformal transformation that will accelerate the convergence. I want to use pade(n-1,n) when I have 2n terms in the power series. But the pade(m,n) throws the above error. It does not seem possible to get a Padé approximation with the same number of coefficients as in the power series.
thanks for taking a look at this. Daniel Friedan
Daniel Friedan
