Theory And Applications Of Special Functions For Scientists And Engineers

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Theory And Applications Of Special Functions For Scientists And Engineers
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Author : Xiao-Jun Yang
language : en
Publisher:
Release Date : 2021
Theory And Applications Of Special Functions For Scientists And Engineers written by Xiao-Jun Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with 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.
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 For Scientists And Engineers
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Author : W. W. Bell
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Special Functions For Scientists And Engineers written by W. W. Bell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Technology & Engineering categories.
This text provides undergraduates with a straightforward guide to special functions. Topics include the solution of 2nd-order differential equations in terms of power series; gamma and beta functions; Legendre polynomials and functions; Bessel functions; Hermite, Laguerre, and Chebyshev polynomials; more. Includes worked examples and problems with some hints and solutions. 1968 edition. 25 figures.
Special Functions For Scientists And Engineers
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Author : W. W. Bell
language : en
Publisher: Courier Corporation
Release Date : 2013-07-24
Special Functions For Scientists And Engineers written by W. W. Bell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-24 with Technology & Engineering categories.
Physics, chemistry, and engineering undergraduates will benefit from this straightforward guide to special functions. Its topics possess wide applications in quantum mechanics, electrical engineering, and many other fields. 1968 edition. Includes 25 figures.
Special Functions For Applied Scientists
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Author : A.M. Mathai
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-13
Special Functions For Applied Scientists 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 2008-02-13 with Science categories.
Chapter 1 introduces elementary classical special functions. Gamma, beta, psi, zeta functions, hypergeometric functions and the associated special functions, generalizations to Meijer's G and Fox's H-functions are examined here. Discussion is confined to basic properties and selected applications. Introduction to statistical distribution theory is provided. Some recent extensions of Dirichlet integrals and Dirichlet densities are discussed. A glimpse into multivariable special functions such as Appell's functions and Lauricella functions is part of Chapter 1. Special functions as solutions of differential equations are examined. Chapter 2 is devoted to fractional calculus. Fractional integrals and fractional derivatives are discussed. Their applications to reaction-diffusion problems in physics, input-output analysis, and Mittag-Leffler stochastic processes are developed. Chapter 3 deals with q-hyper-geometric or basic hypergeometric functions. Chapter 4 covers basic hypergeometric functions and Ramanujan's work on elliptic and theta functions. Chapter 5 examines the topic of special functions and Lie groups. Chapters 6 to 9 are devoted to applications of special functions. Applications to stochastic processes, geometric infinite divisibility of random variables, Mittag-Leffler processes, alpha-Laplace processes, density estimation, order statistics and astrophysics problems, are dealt with in Chapters 6 to 9. Chapter 10 is devoted to wavelet analysis. An introduction to wavelet analysis is given. Chapter 11 deals with the Jacobians of matrix transformations. Various types of matrix transformations and the associated Jacobians are provided. Chapter 12 is devoted to the discussion of functions of matrix argument in the real case. Functions of matrix argument and the pathway models along with their applications are discussed.
The Functions Of Mathematical Physics
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Author : Harry Hochstadt
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
The Functions Of Mathematical Physics written by Harry Hochstadt and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Science categories.
A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.
Introduction To Bessel Functions
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Author : Frank Bowman
language : en
Publisher: Courier Corporation
Release Date : 1958-01-01
Introduction To Bessel Functions written by Frank Bowman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958-01-01 with Mathematics categories.
Self-contained text, useful for classroom or independent study, covers Bessel functions of zero order, modified Bessel functions, definite integrals, asymptotic expansions, and Bessel functions of any real order. 226 problems.
Advanced Mathematical Methods In Science And Engineering
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Author : S.I. Hayek
language : en
Publisher: CRC Press
Release Date : 2010-06-22
Advanced Mathematical Methods In Science And Engineering written by S.I. Hayek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-22 with Mathematics categories.
Classroom-tested, Advanced Mathematical Methods in Science and Engineering, Second Edition presents methods of applied mathematics that are particularly suited to address physical problems in science and engineering. Numerous examples illustrate the various methods of solution and answers to the end-of-chapter problems are included at the back of t
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 Their Applications
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Author : N. N. Lebedev
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
Special Functions Their Applications written by N. N. Lebedev and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.
Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.