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.
Preface; My Thanks to Mourad Ismail for His Work (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 (A 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 Grunbaum, I Pacharoni and I Zurrian); 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, Jesus Guillera, Armin Straub and Wadim Zudilin); Asymptotics of Orthogonal Polynomials and the Painleve Transcendents (Dan Dai); From Gaussian Circle Problem to Multivariate Shannon Sampling (W Freeden, M Z 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); 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);