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Theta functions, elliptic functions and π

Heng Huat Chan (Autor)

Buch | Softcover

XVI, 122 Seiten

2020
De Gruyter (Verlag)
978-3-11-054071-0 (ISBN)

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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.

Heng Huat Chan, National University of Singapore, Singapore.

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

Erscheinungsdatum	08.07.2020
Reihe/Serie	De Gruyter Textbook
Zusatzinfo	4 b/w ill.
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	155 x 230 mm
Gewicht	217 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Eisenstein-Reihe • Elliptische Funktion • Modulform • Pi <Zahl¿ • Pi <Zahl> • Zahlentheorie
ISBN-10	3-11-054071-1 / 3110540711
ISBN-13	978-3-11-054071-0 / 9783110540710
Zustand	Neuware