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.

About the Authors

Howard S. Cohl, National Institute of Standards and Technology, Gaithersburg, MD.

Roberto S. Costas-Santos, Universidad Loyola Andalucia, Sevilla, Spain.

Robert S. Maier, University of Arizona, Tucson, AZ.

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