Bounds on effective moduli by analytical continuation of the Stieltjes function expanded at zero and infinity
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By employing special continued fractions to two Stieltjes series with nonzero radii of convergence the inequalities for two- and three-point Padé approximants have been derived. These inequalities constitute an extension of the relevant relations valid for one-point Padé approximants [1,Cor.17.1] and two-point Padé ones [23, Th.1]. The Padé approximants inequalities achieved have been applied to the theory of inhomogeneous media for establishing of the new bounds on the effective transport coefficient of two-phase composite materials. As an example the low order estimations of the effective conductivity of a square array of cylinders have been computed and compared with the corresponding ones evaluated in .
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