Yattselev, M. L.2023-05-152023-05-152021-11Yattselev, M. L. (2021). Convergence of two-point Padé approximants to piecewise holomorphic functions. Sbornik: Mathematics, 212(11), 1626–1659. https://doi.org/10.1070/SM90241064-5616https://hdl.handle.net/1805/32981Let $f_0$ and $f_\infty$ be formal power series at the origin and infinity, and $P_n/Q_n$, $\deg(P_n),\deg(Q_n)\leq n$, be the rational function that simultaneously interpolates $f_0$ at the origin with order $n$ and $f_\infty$ at infinity with order ${n+1}$. When germs $f_0$ and $f_\infty$ represent multi-valued functions with finitely many branch points, it was shown by Buslaev that there exists a unique compact set $F$ in the complement of which the approximants converge in capacity to the approximated functions. The set $F$ may or may not separate the plane. We study uniform convergence of the approximants for the geometrically simplest sets F that do separate the plane.en-USPublisher Policytwo-point Padé approximantsholomorphic functionsStahl's theoremArticle