Frontiers in Orthogonal Polynomials and q-Series

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 q-series.
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