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

Format:

Book

Author/Creator:

Chan, Heng Huat, author.

Series:

De Gruyter Textbook

Language:

English

Subjects (All):

Functions, Theta.

Physical Description:

1 online resource (XVI, 122 p.)

Place of Publication:

Berlin ; Boston : De Gruyter, [2020]

Language Note:

In English.

Summary:

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.

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

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9783110540758

3110540754

9783110541915

3110541912

OCLC:

1178769537