Ramanujan’s Notebooks, Part 3

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Springer Science & Business Media, Dec 6, 2012 - Mathematics - 510 pages
During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the tasks of editing Ramanujan's notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature.
 

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Contents

Preface
1
CHAPTER
20
CHAPTER 17
34
Fundamental Properties of Elliptic Functions
87
CHAPTER 18
141
CHAPTER 19
220
CHAPTER 20
330
Modular Equations of Higher and Composite Degrees 325
396
CHAPTER 21
449
References
489
Index
505
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