Q Difference Operators Orthogonal Polynomials And Symmetric Expansions

Author : Douglas Bowman
Publisher : American Mathematical Soc.
ISBN 13 : 082182774X
Total Pages : 73 pages
Book Rating : 4.41/5 ( download)

DOWNLOAD NOW!

Download or read book $q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions written by Douglas Bowman and published by American Mathematical Soc.. This book was released on 2002 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Nashed M Zuhair
Publisher : World Scientific
ISBN 13 : 981322889X
Total Pages : 576 pages
Book Rating : 4.94/5 ( download)

DOWNLOAD NOW!

Download or read book Frontiers In Orthogonal Polynomials And Q-series written by Nashed M Zuhair and published by World Scientific. This book was released on 2018-01-12 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : L. Rodman
Publisher : American Mathematical Soc.
ISBN 13 : 0821829963
Total Pages : 87 pages
Book Rating : 4.67/5 ( download)

DOWNLOAD NOW!

Download or read book Abstract Band Method via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation written by L. Rodman and published by American Mathematical Soc.. This book was released on 2002 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, versions of an abstract scheme are developed, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results prove, amongst other things, that the band extension is continuous in an appropriate sense.

Author : Arnd Scheel
Publisher : American Mathematical Soc.
ISBN 13 : 0821833731
Total Pages : 102 pages
Book Rating : 4.35/5 ( download)

DOWNLOAD NOW!

Download or read book Radially Symmetric Patterns of Reaction-Diffusion Systems written by Arnd Scheel and published by American Mathematical Soc.. This book was released on 2003 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.

Author : Eva A. Gallardo-Gutieŕrez
Publisher : American Mathematical Soc.
ISBN 13 : 0821834320
Total Pages : 98 pages
Book Rating : 4.29/5 ( download)

DOWNLOAD NOW!

Download or read book The Role of the Spectrum in the Cyclic Behavior of Composition Operators written by Eva A. Gallardo-Gutieŕrez and published by American Mathematical Soc.. This book was released on 2004 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction and preliminaries Linear fractional maps with an interior fixed point Non elliptic automorphisms The parabolic non automorphism Supercyclic linear fractional composition operators Endnotes Bibliography.

Author : Warren P. Johnson
Publisher : American Mathematical Soc.
ISBN 13 : 1470456230
Total Pages : 519 pages
Book Rating : 4.38/5 ( download)

DOWNLOAD NOW!

Download or read book An Introduction to q-analysis written by Warren P. Johnson and published by American Mathematical Soc.. This book was released on 2020-10-06 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to q q-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.

Author : Yasuyuki Kachi
Publisher : American Mathematical Soc.
ISBN 13 : 0821832255
Total Pages : 133 pages
Book Rating : 4.57/5 ( download)

DOWNLOAD NOW!

Download or read book Segre's Reflexivity and an Inductive Characterization of Hyperquadrics written by Yasuyuki Kachi and published by American Mathematical Soc.. This book was released on 2002 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction The universal pseudo-quotient for a family of subvarieties Normal bundles of quadrics in $X$ Morphisms from quadrics to Grassmannians Pointwise uniform vector bundles on non-singular quadrics Theory of extensions of families over Hilbert schemes Existence of algebraic quotient--proof of Theorem 0.3 Appendix. Deformations of vector bundles on infinitesimally rigid projective varieties with null global $i$-forms References

Author : Jeroen Spandaw
Publisher : American Mathematical Soc.
ISBN 13 : 0821831836
Total Pages : 154 pages
Book Rating : 4.30/5 ( download)

DOWNLOAD NOW!

Download or read book Noether-Lefschetz Problems for Degeneracy Loci written by Jeroen Spandaw and published by American Mathematical Soc.. This book was released on 2003 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the cohomology of degeneracy loci. This title assumes that $E\otimes F DEGREES\vee$ is ample and globally generated, and that $\psi$ is a general homomorphism. In order to study the cohomology of $Z$, it considers the Grassmannian bundle $\pi\colon Y: =\mathbb{G}(f-r, F)\to X$ of $(f-r)$-dimensional linear subspaces of the fibre

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821834452
Total Pages : 102 pages
Book Rating : 4.59/5 ( download)

DOWNLOAD NOW!

Download or read book Exponentially Small Splitting of Invariant Manifolds of Parabolic Points written by and published by American Mathematical Soc.. This book was released on with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821834614
Total Pages : 146 pages
Book Rating : 4.19/5 ( download)

DOWNLOAD NOW!

Download or read book The $RO(G)$-Graded Equivariant Ordinary Homology of $G$-Cell Complexes with Even-Dimensional Cells for $G=\mathbb {Z}/p$ written by and published by American Mathematical Soc.. This book was released on with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: