Theta functions, elliptic functions and π / / Heng Huat Chan.

• Superior document: Title is part of eBook package: De Gruyter DG Ebook Package English 2020
• VerfasserIn: Chan, Heng Huat,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2020]; ©2020
• Year of Publication: 2020
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (XVI, 122 p.)
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110541915; 9783110696288; 9783110696271; 9783110659061; 9783110704716; 9783110704518; 9783110704846; 9783110704662
• DOI: 10.1515/9783110541915
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: 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 included exercises make it ideal for both classroom use and self-study.