BOUNDS ON EFFECTIVE MODULI BY ANALYTICAL CONTINUATION OF THE STIELTJES FUNCTION EXPANDED AT ZERO AND INFINITY

By employing special continued fractions to two Stieltjes series with nonzero radii of convergence the inequalities for two-and three-point Pade approximants have been derived. These inequalities constitute an extension of the relevant relations valid for one-point Pade approxima nts [1,Cor.17.1] and two-point Padi! ones [23, Th.1]. The Padi! approx imants inequalities achieved have been applied to the theory of inhomo geneous media for establishing of the new bounds on tile effective tra nsport coefficient of two-phase composite materials. As an example the low order estimations of tile effective conductivity of a square arra y of cylinders have been computed and compared with the corresponding ones evaluated in [24].