# On continued fractions associated with polynomial type pade approximants, with an application

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## Abstract

The diagonal Padé approximants of power series that satisfy a certain reciprocal property involve, essentially, one polynomial. The continued fractions, whose convergents are the sequence of diagonal approximants, are consequentially of a simplified form. An interesting example is a continued fraction given by Stieltjes, and this is seen to have an application in current approximation theory.

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© Springer-Verlag 1989