Distribution of the zeros of Padé polynomials and analytic continuation

The problem of analytic continuation of a multivalued analytic function with finitely many branch points on the Riemann sphere is discussed. The focus is on Padé approximants: classical (one-point) Padé approximants, multipoint Padé approximants, and Hermite–Padé approximants. The main result is a theorem on the distribution of zeros and the convergence of the Hermite–Padé approximants for a system $[1,f,f^2]$, where $f$ is a multivalued function in the so-called Laguerre class $\mathscr{L}$.
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