Special Functions Of Mathematical Physics
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Special Functions
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Author : Nico M. Temme
language : en
Publisher: John Wiley & Sons
Release Date : 1996-02-22
Special Functions written by Nico M. Temme and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02-22 with Mathematics categories.
This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.
Special Functions Of Mathematical Physics
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Author : NIKIFOROV
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Special Functions Of Mathematical Physics written by NIKIFOROV 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 2013-11-11 with Mathematics categories.
With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan tum mechanics. We have not attempted to provide the most extensive collec tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (§3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (§§12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or thogonal polynomials of a discrete variable on both uniform and nonuniform lattices has been given such a coherent presentation, together with its various applications in physics.
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.
Special Functions
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Author : Nico M. Temme
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01
Special Functions written by Nico M. Temme and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.
This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.
Formulas And Theorems For The Special Functions Of Mathematical Physics
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Author : Wilhelm Magnus
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Formulas And Theorems For The Special Functions Of Mathematical Physics written by Wilhelm Magnus 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 2013-11-11 with Science categories.
This is a new and enlarged English edition of the book which, under the title "Formeln und Satze fur die Speziellen Funktionen der mathe matischen Physik" appeared in German in 1946. Much of the material (part of it unpublished) did not appear in the earlier editions. We hope that these additions will be useful and yet not too numerous for the purpose of locating .with ease any particular result. Compared to the first two (German) editions a change has taken place as far as the list of references is concerned. They are generally restricted to books and monographs and accomodated at the end of each individual chapter. Occasional references to papers follow those results to which they apply. The authors felt a certain justification for this change. At the time of the appearance of the previous edition nearly twenty years ago much of the material was scattered over a number of single contributions. Since then most of it has been included in books and monographs with quite exhaustive bibliographies. For information about numerical tables the reader is referred to "Mathematics of Computation", a periodical publis hed by the American Mathematical Society; "Handbook of Mathe matical Functions" with formulas, graphs and mathematical tables National Bureau of Standards Applied Mathematics Series, 55, 1964, 1046 pp., Government Printing Office, Washington, D.C., and FLETCHER, MILLER, ROSENHEAD, Index of Mathematical Tables, Addison-Wesley, Reading, Mass.) .. There is a list of symbols and abbreviations at the end of the book.
Special Functions Of Mathematical Geo Physics
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Author : Willi Freeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-15
Special Functions Of Mathematical Geo Physics written by Willi Freeden 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 2013-02-15 with Mathematics categories.
Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.
Special Functions
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Author : Sergeĭ I︠U︡rʹevich Slavi︠a︡nov
language : en
Publisher: Oxford University Press, USA
Release Date : 2000
Special Functions written by Sergeĭ I︠U︡rʹevich Slavi︠a︡nov and has been published by Oxford University Press, USA 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 useful text and reference work.
Mathematical Methods In Physics
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Author : Victor Henner
language : en
Publisher: CRC Press
Release Date : 2009-06-18
Mathematical Methods In Physics written by Victor Henner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-18 with Mathematics categories.
This book is a text on partial differential equations (PDEs) of mathematical physics and boundary value problems, trigonometric Fourier series, and special functions. This is the core content of many courses in the fields of engineering, physics, mathematics, and applied mathematics. The accompanying software provides a laboratory environment that
Special Functions In Physics With Matlab
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Author : Wolfgang Schweizer
language : en
Publisher: Springer Nature
Release Date : 2021-03-25
Special Functions In Physics With Matlab written by Wolfgang Schweizer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-25 with Science categories.
This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.
Basic Equations And Special Functions Of Mathematical Physics
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Author : Vasiliĭ I︠A︡kovlevich Arsenin
language : en
Publisher:
Release Date : 1968
Basic Equations And Special Functions Of Mathematical Physics written by Vasiliĭ I︠A︡kovlevich Arsenin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Science categories.