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 recent research on applications of classical hypergeometric and related special functions to problems in mathematical physics and elsewhere, and on $q$-extensions of hypergeometric functions and other topics in $q$-calculus. The problems in mathematical physics include the explicit integration of the stationary SchrOØdinger equation with many potentials and the computation of the gravitational potential of an ellipsoidal mass in terms of elliptic integrals. The $q$-calculus topics include a study of Ramanujan's q- continued fractions and the derivation of new $q$-identities. All research articles come with extensive bibliographies and can serve as entry points to the current literature.
Howard S. Cohl, Roberto S. Costas-Santos, and Robert S. Maier,
Applications
Jan Derezinski, Christian Gas, and Blazej Ruba, Generalized integrals of
Macdonald and Gegenbauer functions
Lina Ellis, Ikumi Ellis, Christoph Koutschan, and Sergei K. Suslov, On
potentials integrated by the Nikoforov-Uvarov method
Jeongsu Kyeong, Irina Mitrea, and Katharine Ott, On the Mellin symbol of
singular integral operators associated with the biharmonic equation in
infinite sectors
Norman Lebovitz, Gravitational potentials of ellipsoidal masses
Iswarya Sitiraju, Spherical distributions on the de Sitter space and their
spectral singularities
Howard S. Cohl, Roberto S. Costas-Santos, and Robert S. Maier,
$q$-extensions
George E. Andrews, The surprising first $q$-Appell function
Gaurav Bhatnagar, Ramanujan's $q$-continued fractions
Howard S. Cohl and Roberto S. Costas-Santos, Orthogonality of the big $-1$
Jacobi polynomials for non-standard parameters
N. Hoshi, M. Katori, T. H. Koornwinder, and M. J. Schlosser, On an identity
of Chaundy and Bullard. III. Basic and elliptic extensions
Timothy Huber, James Mc Laughlin, and Dongxi Ye, Generalizations of some
$q$-product identities of Ramanujan and others
Luis Verde-Star, Discrete orthogonality of the polynomial sequences in the
$q$-Askey scheme
Jianan Xu, Ying Zhang, and Xinrong Ma, A new three-term relation for an
indefinite sum of a very well poised basic hypergeometric series
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
