This question is part of a question on Pade approximants, but I can't see why this is true:
the rational function r_{km}(x)={p_{km}(x) \over {q_{km}(x)} }where p is a poly in x of degree at most k and q is a poly in x of degree at most m, then
f(x)-r(x)=O(x^{k+m+1}), does this not say r has degree k+m? I thought the degree of r is the greater of k & m? This is incorrect?