Some convergence results for the generalized Padé-type approximants
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The aim of this paper is to give some convergence results for some sequences of generalized Padé-type approximants. We will consider two types of interpolatory functionals: one corresponding to Langrange and Hermite interpolation and the other corresponding to orthogonal expansions. For these two cases we will give sufficient conditions on the generating functionG(x, t) and on the linear functionalc in order to obtain the convergence of the corresponding sequence of generalized Padé-type approximants. Some examples are given.
KeywordsOrthogonal polynomials orthogonal expansions Hermite interpolation approximation
AMS subject classification41A05 41A20 42C10 42C05
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