Interpolation and Approximation by Rational Functions in the Complex Domain (COLLOQUIUM PUBLICATIONS (AMER MATHEMATICAL SOC))

J. L. Walsh

ISBN 10: 0821810200 / ISBN 13: 9780821810200

Published by American Mathematical Society, 2008

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Bibliographic Details

Title: Interpolation and Approximation by Rational ...

Publisher: American Mathematical Society

Publication Date: 2008

Binding: Soft cover

Condition: Very Good

Edition: 3rd Edition

About this title

Synopsis:

The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.