| 書目名稱 | Polynomial Expansions of Analytic Functions | | 副標(biāo)題 | Reihe: Moderne Funkt | | 編輯 | Ralph P. Boas,R. Creighton Buck | | 視頻video | http://file.papertrans.cn/752/751340/751340.mp4 | | 叢書名稱 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge | | 圖書封面 |  | | 描述 | 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 [1J, vol. III, chap. 19) and in TRUESDELL [1J. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function j(z) as a series 2::CnPn(z), where {Pn} is a prescribed sequence of functions, and the connections between the function j and the coefficients en. BIEBERBACH‘S mono- graph Analytisehe Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice Pn (z) = zn, 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 applica | | 出版日期 | Book 19581st edition | | 關(guān)鍵詞 | Analytic Functions; Complex analysis; Funktionentheorie; analytic function; function; mathematics | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-87887-9 | | isbn_ebook | 978-3-642-87887-9 | | copyright | Springer-Verlag OHG. Berlin · G?ttingen · Heidelberg 1958 |
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