Some structural properties of two counter-examples to the Baker–Gammel–Wills conjecture

AbstractI improve the counter-example of Lubinsky, and show that the counter-example of Buslaev is also relevant to the original form of the Baker–Gammel–Wills conjecture. I notice that these counter-examples have only a single spurious pole and that a patchwork of just two subsequences of diagonal Padé approximants provides uniform convergence in compact subsets of |z|