Theta functions, elliptic functions and π

Häftad, Engelska, 2020

545 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2020-07-06
Mått:155 x 230 x 8 mm
Vikt:217 g
Format:Häftad
Språk:Engelska
Serie:De Gruyter Textbook
Antal sidor:138
Upplaga:20001
Förlag:De Gruyter
ISBN:9783110540710

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

Heng Huat Chan, National University of Singapore, Singapore.

Innehållsförteckning

IntroductionChapter 1. Euler's identities and Jacobi's triple product identityChapter 2. Jacobi's theta functions and Jacobi' triple product identityChapter 3. Generalization of Jacobi;'s theta functionsChapter 4. Ramanujan's differential equations for Eisenstein seriesChapter 5. The Weierstrass elliptic functionsChapter 6. Jacobi's elliptic functionsChapter 7. Hypergeometric seriesChapter 8. Ramanujan's series for 1/πChapter 9. The Gauss-Brent-Salamin algorithm for πReferences