MARKOV’S PROPERTY AND GENERLIZED PADÉ -TYPE APPROXIMANTS

Abstract

Pade approximants are rational functions whose expansion in ascending powers of the variable coincides with the Taylor power series expansion of analytic functions into a disk as far as possible, that is up to the sum of the degree of the numerator and denominator. The numerator and denominator of a Pade approximant are completely determined by this condition and no freedom is left. On the contrary, Pade-type approximants are rational functions with an arbitrary denominator, whose numerator is determined by the condition that the expansion of the Pade-type approximant matches the Taylor expansion of analytic functions up to the degree of the numerator. The great advantage of Pade-type approximants over Pade approximants lies in the free choice of the poles which may lead to a better approximation ([2-6]).