Counter-examples to the Baker--Gammel--Wills conjecture and patchwork convergence (Q1779430)

This paper is the continuation of the author's investigation. It is connected with the convergence of Padé approximants, several conjectures concerning the pointwise convergence of the diagonal Padé approximants and counter-examples to all of them. All counter-examples correspond to bounded associated continued fractions (Wall's family of complex, bounded \(J\)-matrix). The extended convergence results are given. A new conjecture called patchwork conjecture is proposed. Bibliography contains 18 sources.