### power series method pade(m,n) off by 1?

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 PadÃ© 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 PadÃ© approximation with the same number of coefficients as in the power series.

thanks for taking a look at this.
Daniel Friedan

Daniel Friedan