Description

Book Synopsis
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.

Table of Contents
Generalized Ramanujan Identity; Weierstrass Elliptic Function; Ramanujan's Differential Equations, Ramanujan's 1-Psi-1 Summation Formula; Jacobi Triple Product Identity; Jordan - Kronecker Function; Fundamental Multiplicative Identity; Hypergeometric Functions; Halphen's Differential Equations; Sums of Two and Four Squares; Ramanujan's Theories of Elliptic Functions to Alternative Bases; Jacobian Elliptic Functions; Modular Equations; Addition Theorem for Elliptic Integrals; Quintuple Product Identity.

Development Of Elliptic Functions According To

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    A Hardback by K Venkatachaliengar, Shaun Cooper

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 29 September 2011
      ISBN-13 9789814366458
      978-9814366458
      ISBN-10 9814366455
      Also in:
      Number theory

      Description

      Book Synopsis
      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.

      Table of Contents
      Generalized Ramanujan Identity; Weierstrass Elliptic Function; Ramanujan's Differential Equations, Ramanujan's 1-Psi-1 Summation Formula; Jacobi Triple Product Identity; Jordan - Kronecker Function; Fundamental Multiplicative Identity; Hypergeometric Functions; Halphen's Differential Equations; Sums of Two and Four Squares; Ramanujan's Theories of Elliptic Functions to Alternative Bases; Jacobian Elliptic Functions; Modular Equations; Addition Theorem for Elliptic Integrals; Quintuple Product Identity.

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