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＜E-Book＞
Polynomial expansions of analytic functions / by Ralph P. Boas, Robert Creighton Buck
(Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge ; 19)

Edition	2nd ed. 1964.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1964
Size	VIII, 77 p. 15 illus : online resource
Authors	*Boas, Ralph P author Buck, Robert Creighton author SpringerLink (Online service)
Subjects	LCSH:Functional analysis LCSH:Mathematical analysis FREE:Functional Analysis FREE:Analysis
Notes	I. Introduction -- II. Representation of entire functions -- III. Representation of functions that are regular at the origin -- IV. Applications 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 prop­ 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 mono­ 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 specializa­ 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 HTTP:URL=https://doi.org/10.1007/978-3-662-25170-6

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