Basic inequalities for multipoint Padé approximants to Stieltjes functions

Abstract

Basic inequalities for diagonal and subdiagonal multipoint Padé approximants to N power series expansions of Stieltjes function f₀ at points x₁, x₂,..., x_N are derived. For particular cases the inequalities obtained reduce to those obtained earlier for one-, two- and three-point Padé approximants in [1], [5] and [23], respectively. Numerical examples illustrating the relations achieved are also provided. Our results can be applied to the determination of bounds on the effective moduli of bone subjected to torsion and composites in the case of transport equations.