Theta functions, elliptic functions and π / / Heng Huat Chan.
This book presents several results on elliptic functions and Pi, using Jacobi’s triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan’s work on Pi. The inclu...
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Superior document: | Title is part of eBook package: De Gruyter DG Ebook Package English 2020 |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2020] ©2020 |
Year of Publication: | 2020 |
Language: | English |
Series: | De Gruyter Textbook
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Online Access: | |
Physical Description: | 1 online resource (XVI, 122 p.) |
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Table of Contents:
- Frontmatter
- Contents
- Foreword
- Introduction
- Acknowledgments
- 1 An introduction to Jacobi’s triple product identity
- 2 Jacobi’s theta functions of one variable and the triple product identity
- 3 Two-variable extensions of Jacobi’s theta functions and the partition function
- 4 Ramanujan’s differential equations
- 5 Elliptic functions and Jacobi’s triple product identity
- 6 Two elliptic functions and their properties
- 7 An elliptic function of Jacobi
- 8 Hypergeometric series and Ramanujan’s series 1/π
- 9 The Gauss–Brent–Salamin algorithm for π
- Index
- Bibliography