Theory And Applications Of Special Functions
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Theory And Applications Of Special Functions
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Author : Mourad E. H. Ismail
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Theory And Applications Of Special Functions written by Mourad E. H. Ismail and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
This volume, "Theory and Applications of Special Functions," is d- icated to Mizan Rahman in honoring him for the many important c- tributions to the theory of special functions that he has made over the years, and still continues to make. Some of the papers were presented at a special session of the American Mathematical Society Annual Meeting in Baltimore, Maryland, in January 2003 organized by Mourad Ismail. Mizan Rahman's contributions are not only contained in his own - pers, but also indirectly in other papers for which he supplied useful and often essential information. We refer to the paper on his mathematics in this volume for more information. This paper contains some personal recollections and tries to describe Mizan Rahman's literary writings in his mother tongue, Bengali. An even more personal paper on Mizan Rahman is the letter by his sons, whom we thank for allowing us to reproduce it in this book. The theory of special functions is very much an application driven field of mathematics. This is a very old field, dating back to the 18th century when physicists and mathematician were looking for solutions of the fundamental differential equations of mathematical physics. Since then the field has grown enormously, and this book reflects only part of the known applications.
Special Functions
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Author : George E. Andrews
language : en
Publisher: Cambridge University Press
Release Date : 1999
Special Functions written by George E. Andrews and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
Theory And Applications Of Special Functions For Scientists And Engineers
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Author : Xiao-Jun Yang
language : en
Publisher: Springer
Release Date : 2022-01-14
Theory And Applications Of Special Functions For Scientists And Engineers written by Xiao-Jun Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-14 with Mathematics categories.
This book provides the knowledge of the newly-established supertrigonometric and superhyperbolic functions with the special functions such as Mittag-Leffler, Wiman, Prabhakar, Miller-Ross, Rabotnov, Lorenzo-Hartley, Sonine, Wright and Kohlrausch-Williams-Watts functions, Gauss hypergeometric series and Clausen hypergeometric series. The special functions can be considered to represent a great many of the real-world phenomena in mathematical physics, engineering and other applied sciences. The audience benefits of new and original information and references in the areas of the special functions applied to model the complex problems with the power-law behaviors. The results are important and interesting for scientists and engineers to represent the complex phenomena arising in applied sciences therefore graduate students and researchers in mathematics, physics and engineering might find this book appealing.
The H Function
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Author : A.M. Mathai
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-10
The H Function written by A.M. Mathai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-10 with Science categories.
TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
Special Functions Of Mathematics For Engineers
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Author : Larry C. Andrews
language : en
Publisher: SPIE Press
Release Date : 1998
Special Functions Of Mathematics For Engineers written by Larry C. Andrews and has been published by SPIE Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Modern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science.
Special Functions
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Author : Sergeĭ I︠U︡rʹevich Slavi︠a︡nov
language : en
Publisher: OUP Oxford
Release Date : 2000
Special Functions written by Sergeĭ I︠U︡rʹevich Slavi︠a︡nov and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painlevé equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a valuable text and reference work.
Analytic Number Theory Approximation Theory And Special Functions
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Author : Gradimir V. Milovanović
language : en
Publisher: Springer
Release Date : 2016-09-03
Analytic Number Theory Approximation Theory And Special Functions written by Gradimir V. Milovanović and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-03 with Mathematics categories.
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.
Orthogonal Polynomials And Special Functions
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Author : Francisco Marcellàn
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-19
Orthogonal Polynomials And Special Functions written by Francisco Marcellàn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-19 with Mathematics categories.
Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.
Geometric Theory Of Generalized Functions With Applications To General Relativity
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Author : Michael Grosser
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30
Geometric Theory Of Generalized Functions With Applications To General Relativity written by Michael Grosser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-30 with Mathematics categories.
This work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a `nonlinear distributional geometry' are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject. Audience: The book will be of interest to graduate students as well as to researchers in functional analysis, partial differential equations, differential geometry, and mathematical physics.