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Polynomial expansions of analytic functions / by Ralph P. Boas, Robert Creighton Buck
(Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge ; 19)
版 | 2nd ed. 1964. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 1964 |
大きさ | VIII, 77 p. 15 illus : online resource |
著者標目 | *Boas, Ralph P author Buck, Robert Creighton author SpringerLink (Online service) |
件 名 | LCSH:Functional analysis LCSH:Mathematical analysis FREE:Functional Analysis FREE:Analysis |
一般注記 | 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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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783662251706 |
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EB00204994 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA319-329.9 DC23:515.7 |
書誌ID | 4000110849 |
ISBN | 9783662251706 |
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※2017年9月4日以降