Sixth Summer School, Maryland, 2016

Includes bibliographical references.

Exceptional orthogonal polynomials via Krall discrete polynomials / Antonio J. Duran -- A brief review of q-series / Mourad E.H. Ismail -- Applications of spectral theory to special functions / Erik Koelink -- Elliptic hypergeometric functions / Hjalmar Rosengren -- Combinatorics of orthogonal polynomials and their moments / Jiang Zeng.

"On July 11-15, 2016, we organized a summer school, Orthogonal Polynomials and Special Functions, Summer School 6 (OPSF-S6) which was hosted at the University of Maryland, College Park, Maryland. This summer school was co-organized with Kasso Okoudjou, Professor and Associate Chair, Department of Mathematics, and Norbert Wiener Center for Harmonic Analysis and Applications. OPSF-S6 was a National Science Foundation (NSF) supported summer school on orthogonal polynomials and special functions which received partial support from the Institute forMathematics and its Applications (IMA),Minneapolis, Minnesota. Twenty-two, undergraduates, graduate students, and young researchers attended the summer school from the USA, China, Europe, Morocco and Tunisia, hoping to learn a new state of the art in these subject areas. Since 1970, the subjects of special functions and special families of orthogonal polynomials, have gone through major developments. The Wilson and Askey-Wilson polynomials paved the way for a better understanding of the theory of hypergeometric and basic hypergeometric series and shed new light on the pioneering work of Rogers and Ramanujan. This was combined with advances in the applications of q-series in number theory through the theory of partitions and allied subjects. When quantum groups arrived, the functions which appeared in their representation theory turned out to be the same q-functions which were recently developed at that time. This motivated researchers to revisit the old Bochner problem of studying polynomial solutions to second order differential, difference, or q-difference equations, which are of Sturm-Liouville type and have polynomial coefficients"--