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Polynomial expansions of analytic functions,

Author: Ralph P Boas; R Creighton Buck
Publisher: Berlin, Springer, 1964.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, n. F., Bd. 19.
Edition/Format:   Print book : English : 2nd print. corrView all editions and formats
Summary:
This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal propƯ erties of sets of polynomials which possess simple generating relations.  Read more...
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Additional Physical Format: Online version:
Boas, Ralph Philip.
Polynomial expansions of analytic functions.
Berlin, Springer, 1964
(OCoLC)567905808
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Ralph P Boas; R Creighton Buck
ISBN: 3662251701 9783662251706
OCLC Number: 14246138
Language Note: English.
Description: viii, 77 pages illustrations 24 cm.
Contents: I. Introduction --
II. Representation of entire functions --
III. Representation of functions that are regular at the origin --
IV. Applications.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, n. F., Bd. 19.
Responsibility: by Ralph P. Boas, Jr., and R. Creighton Buck.

Abstract:

This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal propƯ erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series, Lc, . p, . (z), where {p, . } is a prescribed sequence of functions, and the connections between the function f and the coefficients c, . . BIEBERBACH's monoƯ graph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p, . (z) =z", and illustrates the depth and detail which such a specializaƯ tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J.M.

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