Abstract.
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 [24].
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Received: May 20, 1996; revised: April 28, 1997
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Tokarzewski, S., Telega, J. Bounds on effective moduli by analytical continuation of the Stieltjes function expanded at zero and infinity. Z. angew. Math. Phys. 49, 137–155 (1998). https://doi.org/10.1007/s000330050085
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DOI: https://doi.org/10.1007/s000330050085