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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.
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İçerik tablosu
Introduction
Chapter 1. Euler’s identities and Jacobi’s triple product identity
Chapter 2. Jacobi’s theta functions and Jacobi’ triple product identity
Chapter 3. Generalization of Jacobi;’s theta functions
Chapter 4. Ramanujan’s differential equations for Eisenstein series
Chapter 5. The Weierstrass elliptic functions
Chapter 6. Jacobi’s elliptic functions
Chapter 7. Hypergeometric series
Chapter 8. Ramanujan’s series for 1/π
Chapter 9. The Gauss-Brent-Salamin algorithm for π
References
Yazar hakkında
Heng Huat Chan, National University of Singapore, Singapore.
Dil İngilizce ● Biçim EPUB ● Sayfalar 138 ● ISBN 9783110540758 ● Dosya boyutu 14.0 MB ● Yayımcı De Gruyter ● Kent Berlin/Boston ● Yayınlanan 2020 ● Baskı 1 ● İndirilebilir 24 aylar ● Döviz EUR ● Kimlik 7528143 ● Kopya koruma Adobe DRM
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