Description 
1 online resource (xv, 167 pages) : illustrations 
Series 
Monographs in number theory, 17938341 ; v. 6 

Monographs in number theory ; v. 6.

Contents 
88001 The basic identity  The differential equations of P, Q and R  The JordanKronecker function  The Weierstrassian invariants  The Weierstrassian invariants, II  Development of elliptic functions  The modular function [Lambda] 

88001/(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 etafunction  2.5. Notes  3.1. The JordanKronecker 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, 18871920.


Ramanujan Aiyangar, Srinivasa, 18871920 

Elliptic functions.


MATHEMATICS  Complex Analysis.


Elliptic functions

Form 
Electronic book

Author 
Cooper, Shaun

LC no. 
2011293884 
ISBN 
9814366463 

9789814366465 
