The Q Series

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Topics And Methods In Q Series

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Author : James Mc Laughlin
language : en
Publisher: World Scientific
Release Date : 2017-09-22

Topics And Methods In Q Series written by James Mc Laughlin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-22 with Mathematics categories.

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.

An Invitation To Q Series

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Author : Hei-Chi Chan
language : en
Publisher: World Scientific
Release Date : 2011

An Invitation To Q Series written by Hei-Chi Chan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

The aim of this 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.

The Power Of Q

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Author : Michael D. Hirschhorn
language : en
Publisher: Springer
Release Date : 2017-08-08

The Power Of Q written by Michael D. Hirschhorn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-08 with Mathematics categories.

This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and life-long study—inspired by Ramanujan—of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange’s four-squares theorem and Gauss’s two-squares theorem. Attention then turns to partitions and Ramanujan’s partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction, the famous “forty identities” of Ramanujan, and the representation results of Jacobi, Dirichlet and Lorenz, not to mention many other interesting and beautiful results. We also meet a challenge of D.H. Lehmer to give a formula for the number of partitions of a number into four squares, prove a “mysterious” partition theorem of H. Farkas and prove a conjecture of R.Wm. Gosper “which even Erdős couldn’t do.” The book concludes with a look at Ramanujan’s remarkable tau function.

Q Series Their Development And Application In Analysis Number Theory Combinatorics Physics And Computer Algebra

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Author : George E. Andrews
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

Q Series Their Development And Application In Analysis Number Theory Combinatorics Physics And Computer Algebra written by George E. Andrews and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.

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.

The Web Of Modularity Arithmetic Of The Coefficients Of Modular Forms And Q Series

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Author : Ken Ono
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

The Web Of Modularity Arithmetic Of The Coefficients Of Modular Forms And Q Series written by Ken Ono and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

Chapter 1.

Q Series With Applications To Combinatorics Number Theory And Physics

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Author :
language : en
Publisher:
Release Date : 2001

Q Series With Applications To Combinatorics Number Theory And Physics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

Partitions Q Series And Modular Forms

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Author : Krishnaswami Alladi
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-01

Partitions Q Series And Modular Forms written by Krishnaswami Alladi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-01 with Mathematics categories.

Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

Q Series

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Author : George E. Andrews
language : en
Publisher:
Release Date : 1986

Q Series written by George E. Andrews and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with q-series categories.

This book integrates recent developments and related applications in q-series with a historical development of the field, focusing on major breakthroughs and the author's own research interests. The author develops both the important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory. He concludes with applications to physics and computer algebra and a section on results closely related to Ramanujan's "Lost Notebook." With its wide range of applications, the book will interest researchers and students in combinatorics, additive number theo.

The Keeper Of Lost Causes

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Author : Jussi Adler-Olsen
language : en
Publisher: Penguin
Release Date : 2011-08-23

The Keeper Of Lost Causes written by Jussi Adler-Olsen and has been published by Penguin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-23 with Fiction categories.

Get to know the detective in charge of Copenhagen's coldest cases in the first electrifying Department Q mystery from New York Times bestselling author Jussi Adler-Olsen. Carl Mørck used to be one of Denmark’s best homicide detectives. Then a hail of bullets destroyed the lives of two fellow cops, and Carl—who didn’t draw his weapon—blames himself. So a promotion is the last thing he expects. But Department Q is a department of one, and Carl’s got only a stack of cold cases for company. His colleagues snicker, but Carl may have the last laugh, because one file keeps nagging at him: a liberal politician vanished five years earlier and is presumed dead. But she isn’t dead...yet. Darkly humorous, propulsive, and atmospheric, The Keeper of Lost Causes introduces American readers to the mega-bestselling series fast becoming an international sensation.

Reading Frege S Grundgesetze

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Author : Richard G. Heck
language : en
Publisher: Oxford University Press, USA
Release Date : 2012-11-29

Reading Frege S Grundgesetze written by Richard G. Heck and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-29 with Mathematics categories.

Readership: Scholars and advanced students of philosophy of logic, philosophy of mathematics, and history of analytic philosophy