Development of elliptic functions according to Ramanujan /:
This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been i...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2012.
|
| Ausgabe: | [Rev. ed.]. |
| Schriftenreihe: | Monographs in number theory ;
v. 6. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of re. |
| Beschreibung: | Originally published as a Technical Report 2 by Madurai Kamaraj University in February, 1988. |
| Beschreibung: | 1 online resource (xv, 167 pages) : illustrations. |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9814366463 9789814366465 |
| ISSN: | 1793-8341 ; |
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| 245 | 1 | 0 | |a Development of elliptic functions according to Ramanujan / |c originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper. |
| 250 | |a [Rev. ed.]. | ||
| 260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2012. | ||
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| 490 | 1 | |a Monographs in number theory, |x 1793-8341 ; |v v. 6 | |
| 500 | |a Originally published as a Technical Report 2 by Madurai Kamaraj University in February, 1988. | ||
| 505 | 0 | |6 880-01 |a The basic identity -- The differential equations of P, Q and R -- The Jordan-Kronecker function -- The Weierstrassian invariants -- The Weierstrassian invariants, II -- Development of elliptic functions -- The modular function [Lambda]. | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of re. | ||
| 600 | 1 | 0 | |a Ramanujan Aiyangar, Srinivasa, |d 1887-1920. |0 http://id.loc.gov/authorities/names/n50054441 |
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| 650 | 6 | |a Fonctions elliptiques. | |
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| 650 | 7 | |a Elliptic functions |2 fast | |
| 700 | 1 | |a Cooper, Shaun. | |
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| 880 | 0 | |6 505-01/(S |a Machine generated contents note: 1.1. Introduction -- 1.2. The generalized Ramanujan identity -- 1.3. The Weierstrass elliptic function -- 1.4. Notes -- 2.1. Ramanujan's differential equations -- 2.2. Ramanujan's 1ψ1 summation formula -- 2.3. Ramanujan's transcendentals U2n and V2n -- 2.4. The imaginary transformation and Dedekind's eta-function -- 2.5. Notes -- 3.1. The Jordan-Kronecker function -- 3.2. The fundamental multiplicative identity -- 3.3. Partitions -- 3.4. The hypergeometric function 2F1(1/2,1/2;1;x): first method -- 3.5. Notes -- 4.1. Halphen's differential equations -- 4.2. Jacobi's identities and sums of two and four squares -- 4.3. Quadratic transformations -- 4.4. The hypergeometric function 2F1(1/2,1/2;1;x): second method -- 4.5. Notes -- 5.1. Parameterizations of Eisenstein series -- 5.2. Sums of eight squares and sums of eight, triangular numbers -- 5.3. Quadratic transformations -- 5.4. The hypergeometric function 2F1(1/4, 3/4; 1; x). | |
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| _version_ | 1816881784973950976 |
| adam_text | |
| any_adam_object | |
| author | Venkatachaliengar, K. |
| author2 | Cooper, Shaun |
| author2_role | |
| author2_variant | s c sc |
| author_facet | Venkatachaliengar, K. Cooper, Shaun |
| author_role | |
| author_sort | Venkatachaliengar, K. |
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| contents | The basic identity -- The differential equations of P, Q and R -- The Jordan-Kronecker function -- The Weierstrassian invariants -- The Weierstrassian invariants, II -- Development of elliptic functions -- The modular function [Lambda]. |
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| dewey-raw | 515.983 |
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| discipline | Mathematik |
| edition | [Rev. ed.]. |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn774956284 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:14Z |
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| series2 | Monographs in number theory, |
| spelling | Venkatachaliengar, K. Development of elliptic functions according to Ramanujan / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper. [Rev. ed.]. Singapore ; Hackensack, NJ : World Scientific, ©2012. 1 online resource (xv, 167 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Monographs in number theory, 1793-8341 ; v. 6 Originally published as a Technical Report 2 by Madurai Kamaraj University in February, 1988. 880-01 The basic identity -- The differential equations of P, Q and R -- The Jordan-Kronecker function -- The Weierstrassian invariants -- The Weierstrassian invariants, II -- Development of elliptic functions -- The modular function [Lambda]. Includes bibliographical references and index. This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of re. Ramanujan Aiyangar, Srinivasa, 1887-1920. http://id.loc.gov/authorities/names/n50054441 Ramanujan Aiyangar, Srinivasa, 1887-1920 fast https://id.oclc.org/worldcat/entity/E39PBJjtcjjYWv63v7w3DyDrMP Elliptic functions. http://id.loc.gov/authorities/subjects/sh85052336 Fonctions elliptiques. MATHEMATICS Complex Analysis. bisacsh Elliptic functions fast Cooper, Shaun. Print version: 9789814366458 9814366455 (DLC) 2011293884 Monographs in number theory ; v. 6. http://id.loc.gov/authorities/names/no2009064241 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426455 Volltext 505-01/(S Machine generated contents note: 1.1. Introduction -- 1.2. The generalized Ramanujan identity -- 1.3. The Weierstrass elliptic function -- 1.4. Notes -- 2.1. Ramanujan's differential equations -- 2.2. Ramanujan's 1ψ1 summation formula -- 2.3. Ramanujan's transcendentals U2n and V2n -- 2.4. The imaginary transformation and Dedekind's eta-function -- 2.5. Notes -- 3.1. The Jordan-Kronecker function -- 3.2. The fundamental multiplicative identity -- 3.3. Partitions -- 3.4. The hypergeometric function 2F1(1/2,1/2;1;x): first method -- 3.5. Notes -- 4.1. Halphen's differential equations -- 4.2. Jacobi's identities and sums of two and four squares -- 4.3. Quadratic transformations -- 4.4. The hypergeometric function 2F1(1/2,1/2;1;x): second method -- 4.5. Notes -- 5.1. Parameterizations of Eisenstein series -- 5.2. Sums of eight squares and sums of eight, triangular numbers -- 5.3. Quadratic transformations -- 5.4. The hypergeometric function 2F1(1/4, 3/4; 1; x). |
| spellingShingle | Venkatachaliengar, K. Development of elliptic functions according to Ramanujan / Monographs in number theory ; The basic identity -- The differential equations of P, Q and R -- The Jordan-Kronecker function -- The Weierstrassian invariants -- The Weierstrassian invariants, II -- Development of elliptic functions -- The modular function [Lambda]. Ramanujan Aiyangar, Srinivasa, 1887-1920. http://id.loc.gov/authorities/names/n50054441 Ramanujan Aiyangar, Srinivasa, 1887-1920 fast https://id.oclc.org/worldcat/entity/E39PBJjtcjjYWv63v7w3DyDrMP Elliptic functions. http://id.loc.gov/authorities/subjects/sh85052336 Fonctions elliptiques. MATHEMATICS Complex Analysis. bisacsh Elliptic functions fast |
| subject_GND | http://id.loc.gov/authorities/names/n50054441 http://id.loc.gov/authorities/subjects/sh85052336 |
| title | Development of elliptic functions according to Ramanujan / |
| title_auth | Development of elliptic functions according to Ramanujan / |
| title_exact_search | Development of elliptic functions according to Ramanujan / |
| title_full | Development of elliptic functions according to Ramanujan / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper. |
| title_fullStr | Development of elliptic functions according to Ramanujan / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper. |
| title_full_unstemmed | Development of elliptic functions according to Ramanujan / originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper. |
| title_short | Development of elliptic functions according to Ramanujan / |
| title_sort | development of elliptic functions according to ramanujan |
| topic | Ramanujan Aiyangar, Srinivasa, 1887-1920. http://id.loc.gov/authorities/names/n50054441 Ramanujan Aiyangar, Srinivasa, 1887-1920 fast https://id.oclc.org/worldcat/entity/E39PBJjtcjjYWv63v7w3DyDrMP Elliptic functions. http://id.loc.gov/authorities/subjects/sh85052336 Fonctions elliptiques. MATHEMATICS Complex Analysis. bisacsh Elliptic functions fast |
| topic_facet | Ramanujan Aiyangar, Srinivasa, 1887-1920. Ramanujan Aiyangar, Srinivasa, 1887-1920 Elliptic functions. Fonctions elliptiques. MATHEMATICS Complex Analysis. Elliptic functions |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426455 |
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