Topics And Methods In Q Series

Author : James Mc Laughlin
Publisher : World Scientific
Page : 400 pages
File Size : 49,9 Mb
Release : 2017-09-22
Category : Mathematics
ISBN : 9789813223387

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Topics and Methods in q-Series by James Mc Laughlin Pdf

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 : James Mc Laughlin
Publisher : Unknown
Page : 401 pages
File Size : 47,8 Mb
Release : 2017
Category : Electronic books
ISBN : 9813223375

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Topics And Methods In Q-series by James Mc Laughlin Pdf

Author : University of Michigan. College of Engineering
Publisher : UM Libraries
Page : 432 pages
File Size : 44,5 Mb
Release : 1992
Category : Engineering schools
ISBN : UOM:39015023864476

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College of Engineering by University of Michigan. College of Engineering Pdf

Author : Hossein Movasati
Publisher : World Scientific
Page : 323 pages
File Size : 51,7 Mb
Release : 2021-10-12
Category : Mathematics
ISBN : 9789811238697

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Modular And Automorphic Forms & Beyond by Hossein Movasati Pdf

The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.

Author : Dennis Stanton
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468406375

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q-Series and Partitions by Dennis Stanton Pdf

This IMA Volume in Mathematics and its Applications q-Series and Partitions is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizer, Dennis Stanton, for organizing a workshop which brought together many of the major figures in a variety of research fields in which q-series and partitions are used. A vner Friedman Willard Miller, Jr. PREFACE This volume contains the Proceedings of the Workshop on q-Series and Parti tions held at the IMA on March 7-11, 1988. Also included are papers by Goodman and O'Hara, Macdonald, and Zeilberger on unimodality. This work was of substan tial interest and discussed by many participants in the Workshop. The papers have been grouped into four parts: identities, unimodality of Gaus sian polynomials, constant term problems and related integrals, and orthogonal polynomials. They represent a cross section of the recent work on q-series includ ing: partitions, combinatorics, Lie algebras, analysis, and mathematical physics. I would like to thank the staff of the IMA, and its directors, Avner Friedman and Willard Miller, Jr., for providing a wonderful environment for the Workshop. Patricia Brick and Kaye Smith prepared the manuscripts.

Author : University of Michigan
Publisher : UM Libraries
Page : 822 pages
File Size : 49,8 Mb
Release : 1993
Category : Education, Higher
ISBN : UOM:39015078740696

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University of Michigan Official Publication by University of Michigan Pdf

Each number is the catalogue of a specific school or college of the University.

Author : Naihuan Jing,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 44,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821811993

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Recent Developments in Quantum Affine Algebras and Related Topics by Naihuan Jing,Kailash C. Misra Pdf

This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.

Author : Michael D. Hirschhorn
Publisher : Springer
Page : 415 pages
File Size : 52,5 Mb
Release : 2017-08-08
Category : Mathematics
ISBN : 9783319577623

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The Power of q by Michael D. Hirschhorn Pdf

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.

Author : Sergei Suslov
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 54,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475737318

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An Introduction to Basic Fourier Series by Sergei Suslov Pdf

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 : Prof. Anthony Stacey
Publisher : Academic Conferences and publishing limited
Page : 128 pages
File Size : 54,5 Mb
Release : 2019-06-20
Category : Reference
ISBN : 9781912764211

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ECRM 2019 18th European Conference on Research Methods in Business and Management by Prof. Anthony Stacey Pdf

Author : Francisco J. Samaniego,George G. Roussas,Jiming Jiang
Publisher : World Scientific
Page : 479 pages
File Size : 54,6 Mb
Release : 2011-09-16
Category : Mathematics
ISBN : 9789814366564

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Nonparametric Statistical Methods and Related Topics by Francisco J. Samaniego,George G. Roussas,Jiming Jiang Pdf

This volume consists of 22 research papers by leading researchers in Probability and Statistics. Many of the papers are focused on themes that Professor Bhattacharya has published on research. Topics of special interest include nonparametric inference, nonparametric curve fitting, linear model theory, Bayesian nonparametrics, change point problems, time series analysis and asymptotic theory. This volume presents state-of-the-art research in statistical theory, with an emphasis on nonparametric inference, linear model theory, time series analysis and asymptotic theory. It will serve as a valuable reference to the statistics research community as well as to practitioners who utilize methodology in these areas of emphasis.

Author : Andrew Beveridge,Jerrold R. Griggs,Leslie Hogben,Gregg Musiker,Prasad Tetali
Publisher : Springer
Page : 778 pages
File Size : 48,7 Mb
Release : 2016-04-12
Category : Mathematics
ISBN : 9783319242989

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Recent Trends in Combinatorics by Andrew Beveridge,Jerrold R. Griggs,Leslie Hogben,Gregg Musiker,Prasad Tetali Pdf

This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.

Author : Y. Eliashberg,Boris A. Khesin,François Lalonde
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 55,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0821871412

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Symplectic and Contact Topology by Y. Eliashberg,Boris A. Khesin,François Lalonde Pdf

The papers presented in this volume are written by participants of the ''Symplectic and Contact Topology, Quantum Cohomology, and Symplectic Field Theory'' symposium. The workshop was part of a semester-long joint venture of The Fields Institute in Toronto and the Centre de Recherches Mathematiques in Montreal. The twelve papers cover the following topics: Symplectic Topology, the interaction between symplectic and other geometric structures, and Differential Geometry and Topology. The Proceeding concludes with two papers that have a more algebraic character. One is related to the program of Homological Mirror Symmetry: the author defines a category of extended complex manifolds and studies its properties. The subject of the final paper is Non-commutative Symplectic Geometry, in particular the structure of the symplectomorphism group of a non-commutative complex plane. The in-depth articles make this book a useful reference for graduate students as well as research mathematicians.

Author : Vijaya Kumar Murty
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 44,5 Mb
Release : 2010
Category : Coding theory
ISBN : 9780821843116

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Algebraic Curves and Cryptography by Vijaya Kumar Murty Pdf

Focusing on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields the topics covered in this volume include Schoof's $\ell$-adic point counting algorithm, the $p$-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on the Jacobians of $C_{ab}$ curves and zeta functions.

Author : Management Association, Information Resources
Publisher : IGI Global
Page : 663 pages
File Size : 48,9 Mb
Release : 2021-12-30
Category : Science
ISBN : 9781668438824

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Research Anthology on Innovative Research Methodologies and Utilization Across Multiple Disciplines by Management Association, Information Resources Pdf

Research methodology is as old as academia itself. Research methodology shifts in strategy as it crosses different disciplines and theories. This, too, is true with the shifting landscape of research opportunities and technologies available to global researchers. To achieve the most accurate and substantial research, it is important to be knowledgeable of emerging research methodologies. The Research Anthology on Innovative Research Methodologies and Utilization Across Multiple Disciplines discusses the most recent global research innovations made across multiple fields. This anthology further discusses how these research methodologies can be applied to a variety of specific fields. Covering topics such as creative thinking, qualitative research, and the research method landscape, this book is essential for students and faculty of higher education, scientists, researchers, sociologists, computer scientists, and academicians.