Convergence theorems for rows of differential and algebraic Hermite-Padé approximations

摘要

The authors investigate the asymptotic behaviour of Hermite-Padé polynomials of Latin type, which are formed from differential or algebraic expressions involving a meromorphic function. The degrees of the ‘denominator’ polynomials are chosen to correspond to ‘rows’ of the Hermite-Padé table. For special choices of ‘denominator’ degrees, these asymptotic are used to prove de Montessus type theorems for Hermite-Padé approximants formed by solving differential or algebraic equations.