The divergence of the barycentric Padé interpolants

We explain that, like the usual Padé approximants, the barycentric Padé approximants proposed recently by Brezinski and Redivo-Zaglia can diverge. More precisely, we show that for every polynomial P z there exists a function g z = ∑ n = 0 ∞ c n z n , with c n arbitrarily small, such that the sequence of barycentric Padé approximants of f z = P z + g z does not converge uniformly in any subset of C with a non-empty interior.