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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.
€49.95
Table des matières
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
A propos de l’auteur
Heng Huat Chan, National University of Singapore, Singapore.
Langue Anglais ● Format EPUB ● Pages 138 ● ISBN 9783110540758 ● Taille du fichier 14.0 MB ● Maison d’édition De Gruyter ● Lieu Berlin/Boston ● Publié 2020 ● Édition 1 ● Téléchargeable 24 mois ● Devise EUR ● ID 7528143 ● Protection contre la copie Adobe DRM
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