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Author: George E. Andrews
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 144
ISBN-13: 0821807161
DOWNLOAD EBOOKIntegrates 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.
Author: Hei-chi Chan
Publisher: World Scientific
Published: 2011-04-04
Total Pages: 237
ISBN-13: 9814460583
DOWNLOAD EBOOKThe 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.
Author: Ken Ono
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 226
ISBN-13: 0821833685
DOWNLOAD EBOOKChapter 1.
Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
Published: 2011-11-01
Total Pages: 233
ISBN-13: 1461400287
DOWNLOAD EBOOKPartitions, 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.
Author: James Mc Laughlin
Publisher: World Scientific
Published: 2017-09-22
Total Pages: 401
ISBN-13: 9813223383
DOWNLOAD EBOOKThe 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.
Author: Michael D. Hirschhorn
Publisher: Springer
Published: 2017-08-16
Total Pages: 0
ISBN-13: 9783319577616
DOWNLOAD EBOOKThis 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.
Author: Richard G. Heck Jr.
Publisher: OUP Oxford
Published: 2012-11-29
Total Pages: 315
ISBN-13: 019165535X
DOWNLOAD EBOOKGottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy. Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic. Part II examines the mathematical basis of Frege's logicism, explaining and exploring Frege's formal arguments. Heck argues that Frege himself knew that his proofs could be reconstructed so as to avoid Russell's Paradox, and presents Frege's arguments in a way that makes them available to a wide audience. He shows, by example, that careful attention to the structure of Frege's arguments, to what he proved, to how he proved it, and even to what he tried to prove but could not, has much to teach us about Frege's philosophy.
Author: Jussi Adler-Olsen
Publisher: Penguin
Published: 2011-08-23
Total Pages: 453
ISBN-13: 1101543531
DOWNLOAD EBOOKGet 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.
Author: Roland Smith
Publisher: Sleeping Bear Press
Published: 2013-05-20
Total Pages: 242
ISBN-13: 1627531017
DOWNLOAD EBOOKThe president's daughter has been kidnapped by the elusive and lethal Ghost Cell. Quest (Q) and Angela are in hot pursuit with vicious winds and blinding rain thwarting them at every turn. It's a desperate high stakes chase. But who is chasing whom? Are Q and Angela the hunters or the hunted?
Author: George E. Andrews
Publisher: Cambridge University Press
Published: 2004-10-11
Total Pages: 156
ISBN-13: 9780521600903
DOWNLOAD EBOOKProvides a wide ranging introduction to partitions, accessible to any reader familiar with polynomials and infinite series.
