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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
Ã2012.
|
| Colección: | Monographs in number theory ;
v. 6. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Ma 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn794730630 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr buu|||uu||| | ||
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| 050 | 4 | |a QA343 .V46 2012 | |
| 082 | 0 | 4 | |a 515.983 |2 22 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Venkatachaliengar, K. | |
| 245 | 1 | 0 | |a Development of elliptic functions according to Ramanujan / |c originally by K. Venkatachaliengar ; edited and revised by Shaun Cooper. |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific Pub. Co., |c Ã2012. | ||
| 300 | |a 1 online resource (xv, 168 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Monographs in number theory, |x 1793-8341 ; |v v. 6 | |
| 504 | |a Includes bibliographical references (pages 157-163) and index. | ||
| 505 | 0 | |a 1. The Basic Identity. 1.1. Introduction. 1.2. The generalized Ramanujan identity. 1.3. The Weierstrass elliptic function. 1.4. Notes -- 2. The differential equations of P, Q and R. 2.1. Ramanujan's differential equations. 2.2. Ramanujan's [symbol] summation formula. 2.3. Ramanujan's transcendentals U[symbol] and V[symbol]. 2.4. The imaginary transformation and Dedekind's eta-function. 2.5. Notes -- 3. The Jordan-Kronecker Function. 3.1. The Jordan-Kronecker function. 3.2. The fundamental multiplicative identity. 3.3. Partitions. 3.4. The hypergeometric function [symbol](1/2, 1/2; 1; x): first method. 3.5. Notes -- 4. The Weierstrassian invariants. 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 [symbol](1/2, 1/2; 1; x): second method. 4.5. Notes -- 5. The Weierstrassian invariants, II. 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 [symbol](1/4, 3/4; 1; x). 5.5. The hypergeometric function [symbol](1/6, 5/6; 1; x). 5.6. The hypergeometric function [symbol](1/3, 2/3; 1; x). 5.7. Notes -- 6. Development of elliptic functions. 6.1. Introduction. 6.2. Jacobian elliptic functions. 6.3. Reciprocals and quotients. 6.4. Derivatives. 6.5. Addition formulas. 6.6. Notes -- 7. The modular function [symbol]. 7.1. Introduction. 7.2. Modular equations. 7.3. Modular equation of degree 3. 7.4. Modular equation of degree 5. 7.5. Modular equation of degree 7. 7.6. Modular equation of degree 11. 7.7. Modular equation of degree 23. 7.8. Notes. | |
| 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 real and complex analysis. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Elliptic functions. | |
| 650 | 6 | |a Fonctions elliptiques. | |
| 650 | 7 | |a Elliptic functions |2 fast | |
| 700 | 1 | |a Cooper, Shaun. | |
| 710 | 2 | |a World Scientific (Firm) | |
| 758 | |i has work: |a Development of elliptic functions according to Ramanujan (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFwP9fjffjx69jjfqqFD4q |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 1 | |z 9814366455 | |
| 776 | 1 | |z 9789814366458 | |
| 830 | 0 | |a Monographs in number theory ; |v v. 6. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=840716 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL840716 | ||
| 994 | |a 92 |b IZTAP | ||