| Description |
1 online resource (xv, 167 pages) : illustrations |
| Series |
Monographs in number theory, 1793-8341 ; v. 6 |
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Monographs in number theory ; v. 6.
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| Contents |
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] |
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880-01/(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) |
| Summary |
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 |
| Notes |
Originally published as a Technical Report 2 by Madurai Kamaraj University in February, 1988 |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Ramanujan Aiyangar, Srinivasa, 1887-1920.
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Ramanujan Aiyangar, Srinivasa, 1887-1920 |
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Elliptic functions.
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MATHEMATICS -- Complex Analysis.
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Elliptic functions
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| Form |
Electronic book
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| Author |
Cooper, Shaun
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| LC no. |
2011293884 |
| ISBN |
9814366463 |
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9789814366465 |
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