Date: 09 Sep 2006

Padé-type approximants and linear functional transformations

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Let f(.)= \(\mathop \Sigma \limits_{i = o}^\infty\) cigi (.) be a series of functions and let F(.)= \(\mathop \Sigma \limits_{i = o}^\infty\) cihi (.) be the series obtained by applying a linear functional transformation to f. It is shown that the Padé-type approximants of F can be deduced from that of f by application of the same functional transform. Some examples and applications are given. Convergence theorems are obtained. The particular case of the Laplace transform is studied in more detail.