Multivariate homogeneous two-point Padé approximants and continued fractions

Abstract

The multivariate homogeneous two-point Pade approximants have been defined and studied recently. In the current work, we consider higher-order approximants and derive error formulas of these approximants using orthogonality conditions. Diverse three-term recurrence relations satisfied by the monic orthogonal polynomials are presented. Various continued fractions provided by these relations and the quotient-difference algorithm applied to a power series (positive or negative exponents) are described in terms of their relationships with the multivariate homogeneous two-point Pade table. Numerical examples are furnished to illustrate our results.