On the convergence of multi-level Hermite-Padé approximants.

In the present paper we prove a Stieltjes type theorem on the convergence of a sequence of rational functions associated with a mixed type Hermite-Padé approximation problem of a Nikishin system of functions and analyze the ratio asymptotic of the corresponding Hermite-Padé polynomials. • Properties for multi-level Hermite-Padé approximants. • Ratio asymptotic theorem for multi-level Hermite-Padé approximants. • Weak asymptotic theorem for multi-level Hermite-Padé approximants. [ABSTRACT FROM AUTHOR]