Classical Hypergeometric Functions And Generalizations

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Classical Hypergeometric Functions And Generalizations

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Author : Howard S. Cohl
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-23

Classical Hypergeometric Functions And Generalizations written by Howard S. Cohl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-23 with Mathematics categories.

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

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Author : Howard S. Cohl
language : en
Publisher: American Mathematical Society
Release Date : 2025-06-11

Applications And Q Extensions Of Hypergeometric Functions written by Howard S. Cohl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-11 with Mathematics categories.

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

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Author : K. Srinivasa Rao
language : en
Publisher:
Release Date : 2018

Generalized Hypergeometric Functions written by K. Srinivasa Rao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Hypergeometric functions categories.

"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.

Generalized Associated Legendre Functions And Their Applications

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Author : Iryna Fedotova
language : en
Publisher: World Scientific
Release Date : 2001-04-30

Generalized Associated Legendre Functions And Their Applications written by Iryna Fedotova and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-30 with Mathematics categories.

The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions ρFq, Meijer's G-function, Fox's H-function, etc.Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions.This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, Pm,nκ(z) and Qm,nκ(z), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions.The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions Pm,nκ(z) and Qm,nκ(z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+iς(chα) etc.

Special Functions And Generalized Sturm Liouville Problems

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Author : Mohammad Masjed-Jamei
language : en
Publisher: Springer Nature
Release Date : 2020-01-25

Special Functions And Generalized Sturm Liouville Problems written by Mohammad Masjed-Jamei and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-25 with Mathematics categories.

This book discusses theoretical and applied aspects of Sturm-Liouville theory and its generalization. It introduces and classifies generalized Sturm-Liouville problems in three different spaces: continuous, discrete, and q-discrete spaces, focusing on special functions that are solutions of a regular or singular Sturm-Liouville problem. Further, it describes the conditions under which the usual Sturm-Liouville problems with symmetric solutions can be extended to a larger class, particularly highlighting the solutions of generalized problems that result in new orthogonal sequences of continuous or discrete functions. Sturm-Liouville theory is central to problems in many areas, such as engineering, mathematics, physics, and biology. This accessibly written book on the topic is a valuable resource for a broad interdisciplinary readership, from novices to experts.

Generalized Bessel Functions Of The First Kind

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Author : Árpád Baricz
language : en
Publisher: Springer
Release Date : 2010-06-17

Generalized Bessel Functions Of The First Kind written by Árpád Baricz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-17 with Mathematics categories.

In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions.

Algebraic Methods And Q Special Functions

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Author : Jan Felipe Van Diejen
language : en
Publisher: American Mathematical Soc.
Release Date : 1999-01-01

Algebraic Methods And Q Special Functions written by Jan Felipe Van Diejen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.

There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.

Theta Functions Bowdoin 1987 Part 2

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Author : Leon Ehrenpreis
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Theta Functions Bowdoin 1987 Part 2 written by Leon Ehrenpreis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

Invariant Theory

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Author : Robert M. Fossum
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Invariant Theory written by Robert M. Fossum and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

This volume contains the proceedings of the AMS Special Session on Invariant Theory, held in Denton, Texas in the fall of 1986; also included are several invited papers in this area. The purpose of the conference was to exchange ideas on recent developments in algebraic group actions on algebraic varieties. The papers fall into three main categories: actions of linear algebraic groups; flag manifolds and invariant theory; and representation theory and invariant theory. This book is likely to find a wide audience, for invariant theory is connected to a range of mathematical fields, such as algebraic groups, algebraic geometry, commutative algebra, and representation theory.

From Operator Theory To Orthogonal Polynomials Combinatorics And Number Theory

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Author : Fritz Gesztesy
language : en
Publisher: Springer Nature
Release Date : 2021-11-11

From Operator Theory To Orthogonal Polynomials Combinatorics And Number Theory written by Fritz Gesztesy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-11 with Mathematics categories.

The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.