Theta functions, elliptic functions and π

ISBN-13: 9783110540710 / Angielski / Miękka / 2020 / 138 str.

Heng Huat Chan

Opis

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.

Spis treści

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/pi
Chapter 9. The Gauss-Brent-Salamin algorithm for pi
References

O autorze

Heng Huat Chan, National University of Singapore, Singapore.