This volume contains the proceedings of a minisymposium and two AMS special sessions in three conferences: Minisymposium on All Things Hypergeometric, $q$-series and Generalizations at the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-16), June 13-17, 2022, Centre de Recherches Mathematiques, Montreal, Quebec, Canada; AMS Special Session on Hypergeometric Functions and $q$-series at the 2022 AMS Fall Western Sectional Meeting, October 22-23, 2022, University of Utah, Salt Lake City, Utah; and the AMS Special Session on Hypergeometric Functions, $q$-series and Generalizations, at the 2023 AMS Spring Eastern Virtual Sectional Meeting, April 1-2, 2023. This book provides a sampling of current mathematical research related to the Gauss hypergeometric function, and as well, its immediate generalizations and extensions. This includes the generalized hypergeometric functions that originated with Kummer, as well as such classical special functions as Lame and Heun functions. It also includes certain functions relevant to algebraic geometry, such as hypergeometric functions over finite fields. All research articles come with extensive bibliographies and can serve as entry points to the current literature.
Howard S. Cohl, National Institute of Standards and Technology, Gaithersburg, MD, Roberto S. Costas-Santos, Universidad Loyola Andalucia, Sevilla, Spain, and Robert S. Maier, University of Arizona, Tucson, AZ
Hypergeometric functions Asena Cetinkaya and Dmitrii Karp, On digamma series convertible into hypergeometric series Howard S. Cohl, Roberto S. Costas-Santos, Loyal Durand, Camilo Montoya and Gestur Olafsson, Double summation addition theorems for Jacobi functions of the first and second kind Javier Segura, On bounds for ratios of contiguous hypergeometric functions Hans Volkmer, Expansion of the Ferrers function of the first kind in a trigonometric series N. S. Witte, An infinite product of incomplete Beta function-type hypergeometric functions, and its probabilistic origins Generalizations and Extensions Heng Huat Chan and Teoh Guan Chua, The quadratic reciprocity law and the Gauss-Schering lemma Shaun Cooper, Apery-like sequences defined by four-term recurrence relations Yifeng Huang, Ken Ono and Hasan Saad, Counting matrix points on certain varieties over finite fields Eleanor McSpirit and Ken Ono, Hypergeometry and the AGM over finite fields Hans Volkmer, The Heun eigenvalue problem and some of its special cases Yajun Zhou, Hyper-Mahler measures via Goncharov-Deligne cyclotomy
