Inequalities for Two-Point Padé Approximants to the Expansions of Stieltjes Functions in a Real Domain

Abstract

General inequalities satisfied in real domain by two-point Pade approximants (2PPA) to two formal power expansions of Stieltjes functions have been derived. The obtained formulae: (i) generalize the existing inequalities for one-point Pade approximants, (ii) extend the validity of the inequalities reported in J. Comp. Appl. Math. 67 (1996), 59–72, from the particular case 0 ≤ k ≤ 2 to the general case 0 ≤ k ≤ ∞, where (u,k) denotes a given number of coefficients of a power expansion of Stieltjes functions at infinity, (iii) clarify the properties of 2PPA estimations of the effective conductivity for regular composites.