Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions

Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions
Author: Tom H. Koornwinder
Publisher: Cambridge University Press
Total Pages: 442
Release: 2020-10-15
Genre: Mathematics
ISBN: 1108916554

This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

Encyclopedia of Special Functions: The Askey-Bateman Project

Encyclopedia of Special Functions: The Askey-Bateman Project
Author: Tom H. Koornwinder
Publisher: Cambridge University Press
Total Pages: 0
Release: 2020-10-15
Genre: Mathematics
ISBN: 9781107003736

This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

Orthogonal Polynomials of Several Variables

Orthogonal Polynomials of Several Variables
Author: Charles F. Dunkl
Publisher: Cambridge University Press
Total Pages: 439
Release: 2014-08-21
Genre: Mathematics
ISBN: 1107071895

Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.

Special Functions

Special Functions
Author: George E. Andrews
Publisher: Cambridge University Press
Total Pages: 684
Release: 1999
Genre: Mathematics
ISBN: 9780521789882

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

A First Course in Random Matrix Theory

A First Course in Random Matrix Theory
Author: Marc Potters
Publisher: Cambridge University Press
Total Pages: 371
Release: 2020-12-03
Genre: Computers
ISBN: 1108488080

An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.

Reflection Groups and Coxeter Groups

Reflection Groups and Coxeter Groups
Author: James E. Humphreys
Publisher: Cambridge University Press
Total Pages: 222
Release: 1992-10
Genre: Mathematics
ISBN: 9780521436137

This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

A First Course in Fourier Analysis

A First Course in Fourier Analysis
Author: David W. Kammler
Publisher: Cambridge University Press
Total Pages: 39
Release: 2008-01-17
Genre: Mathematics
ISBN: 1139469037

This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

Second Order Differential Equations

Second Order Differential Equations
Author: Gerhard Kristensson
Publisher: Springer Science & Business Media
Total Pages: 225
Release: 2010-08-05
Genre: Mathematics
ISBN: 1441970207

Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusingon the systematic treatment and classification of these solutions. Each chapter contains a set of problems which help reinforce the theory. Some of the preliminaries are covered in appendices at the end of the book, one of which provides an introduction to Poincaré-Perron theory, and the appendix also contains a new way of analyzing the asymptomatic behavior of solutions of differential equations. This textbook is appropriate for advanced undergraduate and graduate students in Mathematics, Physics, and Engineering interested in Ordinary and Partial Differntial Equations. A solutions manual is available online.

General Fractional Derivatives

General Fractional Derivatives
Author: Xiao-Jun Yang
Publisher: CRC Press
Total Pages: 391
Release: 2019-05-10
Genre: Mathematics
ISBN: 0429811527

General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.