Polynomial Expansions of Analytic Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1958
|
| Schriftenreihe: | Ergebnisse der Mathematik und Ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge
19 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 properties 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 monograph 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 specialization 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. |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783642878879 9783642878893 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-87887-9 |
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Datensatz im Suchindex
| _version_ | 1804153098408558592 |
|---|---|
| any_adam_object | |
| author | Boas, Ralph P. |
| author_facet | Boas, Ralph P. |
| author_role | aut |
| author_sort | Boas, Ralph P. |
| author_variant | r p b rp rpb |
| building | Verbundindex |
| bvnumber | BV042423083 |
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| ctrlnum | (OCoLC)1185154285 (DE-599)BVBBV042423083 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-87887-9 |
| format | Electronic eBook |
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| id | DE-604.BV042423083 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642878879 9783642878893 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858500 |
| oclc_num | 1185154285 |
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| publishDate | 1958 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Ergebnisse der Mathematik und Ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge |
| spelling | Boas, Ralph P. Verfasser aut Polynomial Expansions of Analytic Functions by Ralph P. Boas, R. Creighton Buck Berlin, Heidelberg Springer Berlin Heidelberg 1958 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und Ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge 19 0071-1136 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 properties 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 monograph 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 specialization 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. Mathematics Mathematics, general Mathematik Polynomerweiterung (DE-588)4175261-2 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 s Polynom (DE-588)4046711-9 s 1\p DE-604 Polynomerweiterung (DE-588)4175261-2 s 2\p DE-604 Holomorphe Funktion (DE-588)4025645-5 s 3\p DE-604 Approximationstheorie (DE-588)4120913-8 s 4\p DE-604 Buck, R. Creighton Sonstige oth https://doi.org/10.1007/978-3-642-87887-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Boas, Ralph P. Polynomial Expansions of Analytic Functions Mathematics Mathematics, general Mathematik Polynomerweiterung (DE-588)4175261-2 gnd Approximationstheorie (DE-588)4120913-8 gnd Analytische Funktion (DE-588)4142348-3 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Polynom (DE-588)4046711-9 gnd |
| subject_GND | (DE-588)4175261-2 (DE-588)4120913-8 (DE-588)4142348-3 (DE-588)4025645-5 (DE-588)4046711-9 |
| title | Polynomial Expansions of Analytic Functions |
| title_auth | Polynomial Expansions of Analytic Functions |
| title_exact_search | Polynomial Expansions of Analytic Functions |
| title_full | Polynomial Expansions of Analytic Functions by Ralph P. Boas, R. Creighton Buck |
| title_fullStr | Polynomial Expansions of Analytic Functions by Ralph P. Boas, R. Creighton Buck |
| title_full_unstemmed | Polynomial Expansions of Analytic Functions by Ralph P. Boas, R. Creighton Buck |
| title_short | Polynomial Expansions of Analytic Functions |
| title_sort | polynomial expansions of analytic functions |
| topic | Mathematics Mathematics, general Mathematik Polynomerweiterung (DE-588)4175261-2 gnd Approximationstheorie (DE-588)4120913-8 gnd Analytische Funktion (DE-588)4142348-3 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Polynom (DE-588)4046711-9 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Polynomerweiterung Approximationstheorie Analytische Funktion Holomorphe Funktion Polynom |
| url | https://doi.org/10.1007/978-3-642-87887-9 |
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