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Invitation To Q-series, An: From Jacobi's Triple Product Identity To Ramanujan's "Most Beautiful Identity"

2011-04-04 Mathematics
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Release : 2011-04-04
Genre : Mathematics
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Book Rating : 583/5 ( reviews)

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Book Synopsis Invitation To Q-series, An: From Jacobi's Triple Product Identity To Ramanujan's "Most Beautiful Identity" by : Hei-chi Chan

Download or read book Invitation To Q-series, An: From Jacobi's Triple Product Identity To Ramanujan's "Most Beautiful Identity" written by Hei-chi Chan. This book was released on 2011-04-04. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G. H. Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.

$q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra

1986 Mathematics
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Release : 1986
Genre : Mathematics
Kind : eBook
Book Rating : 161/5 ( reviews)

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Book Synopsis $q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra by : George E. Andrews

Download or read book $q$-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra written by George E. Andrews. This book was released on 1986. Available in PDF, EPUB and Kindle. Book excerpt: Integrates developments and related applications in $q$-series with a historical development of the field. This book develops important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory.

Topics And Methods In Q-series

2017-09-22 Mathematics
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Release : 2017-09-22
Genre : Mathematics
Kind : eBook
Book Rating : 383/5 ( reviews)

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Book Synopsis Topics And Methods In Q-series by : James Mc Laughlin

Download or read book Topics And Methods In Q-series written by James Mc Laughlin. This book was released on 2017-09-22. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive introduction to the many aspects of the subject of basic hypergeometric series. The book essentially assumes no prior knowledge but eventually provides a comprehensive introduction to many important topics. After developing a treatment of historically important topics such as the q-binomial theorem, Heine's transformation, the Jacobi triple product identity, Ramanujan's 1-psi-1 summation formula, Bailey's 6-psi-6 summation formula and the Rogers-Fine identity, the book goes on to delve more deeply into important topics such as Bailey- and WP-Bailey pairs and chains, q-continued fractions, and mock theta functions. There are also chapters on other topics such as Lambert series and combinatorial proofs of basic hypergeometric identities.The book could serve as a textbook for the subject at the graduate level and as a textbook for a topic course at the undergraduate level (earlier chapters). It could also serve as a reference work for researchers in the area.

The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series

2004 Mathematics
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Release : 2004
Genre : Mathematics
Kind : eBook
Book Rating : 685/5 ( reviews)

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Book Synopsis The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series by : Ken Ono

Download or read book The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series written by Ken Ono. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1.

An Introduction to q-analysis

2020-10-06 Education
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Release : 2020-10-06
Genre : Education
Kind : eBook
Book Rating : 230/5 ( reviews)

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Book Synopsis An Introduction to q-analysis by : Warren P. Johnson

Download or read book An Introduction to q-analysis written by Warren P. Johnson. This book was released on 2020-10-06. Available in PDF, EPUB and Kindle. Book excerpt: Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to q q-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.

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