Author: James Mc Laughlin
Publisher: World Scientific
ISBN: 9813223383
Category : Mathematics
Languages : en
Pages : 401
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Book Description
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.
Author: Hei-chi Chan
Publisher: World Scientific
ISBN: 9814460583
Category : Mathematics
Languages : en
Pages : 237
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Book Description
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.
Author: James Mc Laughlin
Publisher:
ISBN: 9789813223370
Category : Electronic books
Languages : en
Pages : 401
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Book Description
Author: Bruce McKeown
Publisher: SAGE Publications
ISBN: 148332284X
Category : Psychology
Languages : en
Pages : 121
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Book Description
Direct, well-organized, and easy to follow, Q Methodology, Second Edition, by Bruce McKeown and Dan B. Thomas, reviews the philosophical foundations of subjective communicability (concourse theory), operant subjectivity, and quantum-theoretical aspects of Q as relevant to the social and behavioral sciences. The authors discuss data-gathering techniques (communication concourses, Q samples, and Q sorting), statistical techniques (correlation and factor analysis and the important calculation of factor scores), and strategies for conducting small person-sample research along Q methodological lines.
Author: George E Andrews
Publisher: World Scientific
ISBN: 9811277389
Category : Mathematics
Languages : en
Pages : 704
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Book Description
This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.
Author: University of Michigan
Publisher: UM Libraries
ISBN:
Category : Education, Higher
Languages : en
Pages : 822
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Book Description
Each number is the catalogue of a specific school or college of the University.
Author: University of Michigan. College of Engineering
Publisher: UM Libraries
ISBN:
Category : Engineering schools
Languages : en
Pages : 432
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Book Description
Author: Simon Watts
Publisher: SAGE
ISBN: 1446290700
Category : Reference
Languages : en
Pages : 251
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Book Description
This book is a simple yet thorough introduction to Q methodology, a research technique designed to capture the subjective or first-person viewpoints of its participants. Watts and Stenner outline the key theoretical concepts developed by William Stephenson, the founder of Q methodology, including subjectivity, concourse theory and abduction. They then turn to the practicalities of delivering high quality Q methodological research. Using worked examples throughout, the reader is guided through: • important design issues • the conduct of fieldwork • all the analytic processes of Q methodology, including factor extraction, factor rotation and factor interpretation. Drawing on helpful conceptual introductions to potentially difficult statistical concepts and a step-by-step guide to running Q methodological analyses using dedicated software, this book enables interested readers to design, manage, analyse, interpret and publish their own Q methodological research.
Author: Sergei Suslov
Publisher: Springer Science & Business Media
ISBN: 1475737319
Category : Mathematics
Languages : en
Pages : 379
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Book Description
It was with the publication of Norbert Wiener's book ''The Fourier In tegral and Certain of Its Applications" [165] in 1933 by Cambridge Univer sity Press that the mathematical community came to realize that there is an alternative approach to the study of c1assical Fourier Analysis, namely, through the theory of c1assical orthogonal polynomials. Little would he know at that time that this little idea of his would help usher in a new and exiting branch of c1assical analysis called q-Fourier Analysis. Attempts at finding q-analogs of Fourier and other related transforms were made by other authors, but it took the mathematical insight and instincts of none other then Richard Askey, the grand master of Special Functions and Orthogonal Polynomials, to see the natural connection between orthogonal polynomials and a systematic theory of q-Fourier Analysis. The paper that he wrote in 1993 with N. M. Atakishiyev and S. K Suslov, entitled "An Analog of the Fourier Transform for a q-Harmonic Oscillator" [13], was probably the first significant publication in this area. The Poisson k~rnel for the contin uous q-Hermite polynomials plays a role of the q-exponential function for the analog of the Fourier integral under considerationj see also [14] for an extension of the q-Fourier transform to the general case of Askey-Wilson polynomials. (Another important ingredient of the q-Fourier Analysis, that deserves thorough investigation, is the theory of q-Fourier series.
Author: Michael D. Hirschhorn
Publisher: Springer
ISBN: 9783319577616
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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.
