Frontiers In Orthogonal Polynomials And Q-series

Frontiers In Orthogonal Polynomials And Q-series

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Overview

Frontiers In Orthogonal Polynomials And Q-series by M Zuhair Nashed

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.

Product Details

ISBN-13: 9789813228870
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 02/28/2018
Series: Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes Series , #1
Pages: 576
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

Table of Contents

Preface

About the Editors ix

1 Mourad Ismail Richard Askey 1

2 Binomial Andrews-Gordon-Bressoud Identities Dennis Stanton 7

3 Symmetric Expansions of Very Well-Poised Basic Hypergeometric Series George E. Andrews 21

4 A Sturm-Liouville Theory for Hahn Difference Operator M. H. Annaby A. E. Hamza S. D. Makharesh 35

5 Solvability of the Hankel Determinant Problem for Real Sequences Andrew Bakan Christian Berg 85

6 Convolution and Product Theorems for the Special Affine Fourier Transform Ayush Bhandari Ahmed I. Zayed 119

7 A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials M. Castro F. A. Grünbaum I. Pacharoni I. Zurrián 139

8 The Orthogonality of Al-Salam-Carlitz Polynomials for Complex Parameters Howard S. Cohl Roberto S. Costas-Santos Wenqing Xu 155

9 Crouching AGM, Hidden Modularity Shaun Cooper Jesús Guillera Armin Straub Wadim Zudilin 169

10 Asymptotics of Orthogonal Polynomials and the Painlevé Transcendents Dan Dai 189

11 From the Gaussian Circle Problem to Multivariate Shannon Sampling Willi Freeden M. Zuhair Nashed 213

12 Weighted Partition Identities and Divisor Sums F.G. Garvan 239

13 On the Ismail-Letcssicr-Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials Walter Gautschi 251

14 A Discrete Top-Down Markov Problem in Approximation Theory Walter Gautschi 267

15 Super symmetry of the Quantum Rotor Vincent X. Genest Luc Vinet Guo-Fu Yu Alexei Zhedanov 291

16 The Method of Brackets in Experimental Mathematics Ivan Gonzalez Karen Kohl Lin Jiu Victor H. Moll 307

17 Balanced Modular Parameterizations Tim Huber Danny Lara Esteban Melendez 319

18 Some Smallest Parts Functions from Variations of Bailey's Lemma Chris Jennings-Shaffer 343

19 Dual Addition Formulas Associated with Dual Product Formulas Torn H. Koornwinder 373

20 Holonomic Tools for Basic Hypergeometric Functions Christoph Koutschan Peter Paule 393

21 A Direct Evaluation of an Integral of Ismail and Valent Alexey Kuznetsov 417

22 Algebraic Generating Functions for Gegenbauer Polynomials Robert S. Maier 425

23 q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey Michael J. Schlosser 445

24 Summation Formulas for Noncommutative Hypergeometric Series Michael J. Schlosser 451

25 Asymptotics of Generalized Hypergeometric Functions Y. Lin R. Wong 497

26 Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell-Lerch Series Changgui Zhang 523

27 Certain Positive Semidefinite Matrices of Special Functions Ruiming Zhang 545

Index 557

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