Frontiers In Orthogonal Polynomials And Q Series

Author : Nashed M Zuhair,Li Xin
Publisher : World Scientific
Page : 576 pages
File Size : 50,6 Mb
Release : 2018-01-12
Category : Mathematics
ISBN : 9789813228894

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Frontiers In Orthogonal Polynomials And Q-series by Nashed M Zuhair,Li Xin Pdf

This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10–12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday. The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate. Contents: Mourad Ismail (Richard Askey)Binomial Andrews–Gordon–Bressoud Identities (Dennis Stanton)Symmetric Expansions of Very Well-Poised Basic Hypergeometric Series (George E Andrews)A Sturm–Liouville Theory for Hahn Difference Operator (M H Annaby, A E Hamza and S D Makharesh)Solvability of the Hankel Determinant Problem for Real Sequences (Andrew Bakan and Christian Berg)Convolution and Product Theorems for the Special Affine Fourier Transform (Ayush Bhandari and Ahmed I Zayed)A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials (M Castro, F A Grünbaum, I Pacharoni and I Zurrián)The Orthogonality of Al–Salam–Carlitz Polynomials for Complex Parameters (Howard S Cohl, Roberto S Costas-Santos and Wenqing Xu)Crouching AGM, Hidden Modularity (Shaun Cooper, Jesús Guillera, Armin Straub and Wadim Zudilin)Asymptotics of Orthogonal Polynomials and the Painlevé Transcendents (Dan Dai)From the Gaussian Circle Problem to Multivariate Shannon Sampling (Willi Freeden and M Zuhair Nashed)Weighted Partition Identities and Divisor Sums (F G Garvan)On the Ismail–Letessier–Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials (Walter Gautschi)A Discrete Top-Down Markov Problem in Approximation Theory (Walter Gautschi)Supersymmetry of the Quantum Rotor (Vincent X Genest, Luc Vinet, Guo-Fu Yu and Alexei Zhedanov)The Method of Brackets in Experimental Mathematics (Ivan Gonzalez, Karen Kohl, Lin Jiu and Victor H Moll)Balanced Modular Parameterizations (Tim Huber, Danny Lara and Esteban Melendez)Some Smallest Parts Functions from Variations of Bailey's Lemma (Chris Jennings-Shaffer)Dual Addition Formulas Associated with Dual Product Formulas (Tom H Koornwinder)Holonomic Tools for Basic Hypergeometric Functions (Christoph Koutschan and Peter Paule)A Direct Evaluation of an Integral of Ismail and Valent (Alexey Kuznetsov)Algebraic Generating Functions for Gegenbauer Polynomials (Robert S Maier)q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey (Michael J Schlosser)Summation Formulae for Noncommutative Hypergeometric Series (Michael J Schlosser)Asymptotics of Generalized Hypergeometric Functions (Y Lin and R Wong)Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell–Lerch Series (Changgui Zhang)On Certain Positive Semidefinite Matrices of Special Functions (Ruiming Zhang) Readership: Graduate students and researchers interested in orthogonal polynomials and

Author : M. Zuhair Nashed,李欣
Publisher : Unknown
Page : 0 pages
File Size : 52,8 Mb
Release : 2022
Category : Orthogonal polynomials
ISBN : 7576703741

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Frontiers in Orthogonal Polynomials and Q-series by M. Zuhair Nashed,李欣 Pdf

Author : Roelof Koekoek,Peter A. Lesky,René F. Swarttouw
Publisher : Springer Science & Business Media
Page : 584 pages
File Size : 51,6 Mb
Release : 2010-03-18
Category : Mathematics
ISBN : 9783642050145

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Hypergeometric Orthogonal Polynomials and Their q-Analogues by Roelof Koekoek,Peter A. Lesky,René F. Swarttouw Pdf

The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).

Author : Howard S. Cohl,Mourad E. H. Ismail
Publisher : Cambridge University Press
Page : 351 pages
File Size : 41,5 Mb
Release : 2020-10-15
Category : Mathematics
ISBN : 9781108821599

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Lectures on Orthogonal Polynomials and Special Functions by Howard S. Cohl,Mourad E. H. Ismail Pdf

Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.

Author : Douglas Bowman
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 53,5 Mb
Release : 2002
Category : Difference operators
ISBN : 9780821827741

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$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions by Douglas Bowman Pdf

The author explores ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also found. This provides a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. Some infrastructure is also laid for more general investigations in the future

Author : Jan Felipe Van Diejen,Luc Vinet
Publisher : American Mathematical Soc.
Page : 302 pages
File Size : 48,5 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 0821873296

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Algebraic Methods and Q-special Functions by Jan Felipe Van Diejen,Luc Vinet Pdf

There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.

Author : Jan Felipe Van Diejen,Luc Vinet
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 54,9 Mb
Release : 1999
Category : Fonctions spéciales - Congrès
ISBN : 9780821820261

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Algebraic Methods and $q$-Special Functions by Jan Felipe Van Diejen,Luc Vinet Pdf

There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.

Author : Richard Askey,James Arthur Wilson
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 55,8 Mb
Release : 1985-12-31
Category : Mathematics
ISBN : 0821860550

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Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials by Richard Askey,James Arthur Wilson Pdf

Author : Paul G. Nevai
Publisher : American Mathematical Soc.
Page : 185 pages
File Size : 52,7 Mb
Release : 1979
Category : Orthogonal polynomials
ISBN : 9780821822135

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Orthogonal Polynomials by Paul G. Nevai Pdf

Author : Diego Dominici,Robert Sullivan Maier
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 51,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821846506

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Special Functions and Orthogonal Polynomials by Diego Dominici,Robert Sullivan Maier Pdf

"This volume contains fourteen articles that represent the AMS Special Session on Special Functions and Orthogonal Polynomials, held in Tucson, Arizona in April of 2007. It gives an overview of the modern field of special functions with all major subfields represented, including: applications to algebraic geometry, asymptotic analysis, conformal mapping, differential equations, elliptic functions, fractional calculus, hypergeometric and q-hypergeometric series, nonlinear waves, number theory, symbolic and numerical evaluation of integrals, and theta functions. A few articles are expository, with extensive bibliographies, but all contain original research." "This book is intended for pure and applied mathematicians who are interested in recent developments in the theory of special functions. It covers a wide range of active areas of research and demonstrates the vitality of the field."--BOOK JACKET.

Author : George Gasper,Mizan Rahman
Publisher : Cambridge University Press
Page : 456 pages
File Size : 55,8 Mb
Release : 2004-10-04
Category : Mathematics
ISBN : 9780521833578

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Basic Hypergeometric Series by George Gasper,Mizan Rahman Pdf

This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained, and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series. Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its strengths. The first five chapters cover basic hypergeometric series and integrals, whilst the next five are devoted to applications in various areas including Askey-Wilson integrals and orthogonal polynomials, partitions in number theory, multiple series, orthogonal polynomials in several variables, and generating functions. Chapters 9-11 are new for the second edition, the final chapter containing a simplified version of the main elements of the theta and elliptic hypergeometric series as a natural extension of the single-base q-series. Some sections and exercises have been added to reflect recent developments, and the Bibliography has been revised to maintain its comprehensiveness.

Author : Krishnaswami Alladi,Bruce C. Berndt,Peter Paule,James A. Sellers,Ae Ja Yee
Publisher : Springer Nature
Page : 810 pages
File Size : 55,7 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9783030570507

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George E. Andrews 80 Years of Combinatory Analysis by Krishnaswami Alladi,Bruce C. Berndt,Peter Paule,James A. Sellers,Ae Ja Yee Pdf

This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.

Author : Walter Gautschi
Publisher : Oxford University Press on Demand
Page : 301 pages
File Size : 53,5 Mb
Release : 2004
Category : Mathematics
ISBN : 0198506724

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Orthogonal Polynomials by Walter Gautschi Pdf

This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.

Author : Ugo Bruzzo,Beatriz Grana Otero
Publisher : World Scientific
Page : 214 pages
File Size : 54,6 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9789811207303

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Derived Functors And Sheaf Cohomology by Ugo Bruzzo,Beatriz Grana Otero Pdf

The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra.The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors are stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Čech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter.

Author : Tzuong-tsieng Moh
Publisher : World Scientific
Page : 266 pages
File Size : 51,9 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9789811220982

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Introduction To Algebraic Coding Theory by Tzuong-tsieng Moh Pdf

In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.