Classical Hypergeometric Functions And Generalizations
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Classical Hypergeometric Functions and Generalizations
Author: Howard S. Cohl
language: en
Publisher: American Mathematical Society
Release Date: 2025-04-23
This is the first volume of a two-volume collection of recent research results related to hypergeometric functions. The second volume (Contemporary Mathematics, Volume 819) is titled Applications and $q$-Extensions of Hypergeometric Functions. 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 Mathématiques, Montréal, Québec, 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 Lamé 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.
Applications and $q$-Extensions of Hypergeometric Functions
Author: Howard S. Cohl
language: en
Publisher: American Mathematical Society
Release Date: 2025-06-11
This is the second volume of a two-volume collection of recent research results related to hypergeometric functions. The first volume (Contemporary Mathematics, Volume 818) is titled Classical Hypergeometric Functions and Generalizations. 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 Mathématiques, Montréal, Québec, 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 Schrödinger 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, new $q$-identities, and important limits of basic hypergeometric orthogonal polynomials. All research articles come with extensive bibliographies and can serve as entry points to the current literature.
Generalized Hypergeometric Functions
"In 1813, Gauss first outlined his studies of the hypergeometric series which has been of great significance in the mathematical modelling of physical phenomena. This detailed monograph outlines the fundamental relationships between the hypergeometric function and special functions. In nine comprehensive chapters, Dr. Rao and Dr. Lakshminarayanan present a unified approach to the study of special functions of mathematics using Group theory. The book offers fresh insight into various aspects of special functions and their relationship, utilizing transformations and group theory and their applications. It will lay the foundation for deeper understanding by both experienced researchers and novice students." -- Prové de l'editor.