Theta functions, elliptic functions and π / / Heng Huat Chan.
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 inclu...
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| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2020] ©2020 |
| Year of Publication: | 2020 |
| Language: | English |
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| Physical Description: | 1 online resource (XVI, 122 p.) |
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Chan, Heng Huat, author. aut http://id.loc.gov/vocabulary/relators/aut Theta functions, elliptic functions and π / Heng Huat Chan. Berlin ; Boston : De Gruyter, [2020] ©2020 1 online resource (XVI, 122 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 27. Jan 2023) Elliptic functions. Functions, Theta. Pi. Eisenstein-Reihe. Elliptische Funktion. Modulform. Pi ‹Zahl›. Zahlentheorie. Title is part of eBook package: De Gruyter DG Ebook Package English 2020 9783110696288 Title is part of eBook package: De Gruyter DG Plus DeG Package 2020 Part 1 9783110696271 Title is part of eBook package: De Gruyter De Gruyter English eBooks 2020 - UC 9783110659061 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English 9783110704716 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 9783110704518 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2020 English 9783110704846 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2020 9783110704662 ZDB-23-DMA EPUB 9783110540758 print 9783110540710 https://doi.org/10.1515/9783110541915 https://www.degruyter.com/isbn/9783110541915 Cover https://www.degruyter.com/document/cover/isbn/9783110541915/original |
| language |
English |
| format |
eBook |
| author |
Chan, Heng Huat, Chan, Heng Huat, |
| spellingShingle |
Chan, Heng Huat, Chan, Heng Huat, Theta functions, elliptic functions and π / De Gruyter Textbook 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 |
| author_facet |
Chan, Heng Huat, Chan, Heng Huat, |
| author_variant |
h h c hh hhc h h c hh hhc |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
Chan, Heng Huat, |
| title |
Theta functions, elliptic functions and π / |
| title_full |
Theta functions, elliptic functions and π / Heng Huat Chan. |
| title_fullStr |
Theta functions, elliptic functions and π / Heng Huat Chan. |
| title_full_unstemmed |
Theta functions, elliptic functions and π / Heng Huat Chan. |
| title_auth |
Theta functions, elliptic functions and π / |
| title_alt |
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 |
| title_new |
Theta functions, elliptic functions and π / |
| title_sort |
theta functions, elliptic functions and π / |
| series |
De Gruyter Textbook |
| series2 |
De Gruyter Textbook |
| publisher |
De Gruyter, |
| publishDate |
2020 |
| physical |
1 online resource (XVI, 122 p.) Issued also in print. |
| 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 |
| isbn |
9783110541915 9783110696288 9783110696271 9783110659061 9783110704716 9783110704518 9783110704846 9783110704662 9783110540758 9783110540710 |
| url |
https://doi.org/10.1515/9783110541915 https://www.degruyter.com/isbn/9783110541915 https://www.degruyter.com/document/cover/isbn/9783110541915/original |
| illustrated |
Not Illustrated |
| doi_str_mv |
10.1515/9783110541915 |
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1178769537 |
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AT chanhenghuat thetafunctionsellipticfunctionsandp |
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Title is part of eBook package: De Gruyter DG Ebook Package English 2020 Title is part of eBook package: De Gruyter DG Plus DeG Package 2020 Part 1 Title is part of eBook package: De Gruyter De Gruyter English eBooks 2020 - UC Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2020 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2020 |
| is_hierarchy_title |
Theta functions, elliptic functions and π / |
| container_title |
Title is part of eBook package: De Gruyter DG Ebook Package English 2020 |
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1806144449828356096 |
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