Formulas And Theorems For The Special Functions Of Mathematical Physics

Author : Wilhelm Magnus,Fritz Oberhettinger,Raj Pal Soni
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 45,6 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783662117613

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Formulas and Theorems for the Special Functions of Mathematical Physics by Wilhelm Magnus,Fritz Oberhettinger,Raj Pal Soni Pdf

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 Much of the material (part of it unpublished) did not appear in the earlier editions.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.

Author : Nico M. Temme
Publisher : John Wiley & Sons
Page : 398 pages
File Size : 49,6 Mb
Release : 1996-02-22
Category : Mathematics
ISBN : 0471113131

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Special Functions by Nico M. Temme Pdf

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.

Author : Harry Hochstadt
Publisher : Courier Corporation
Page : 354 pages
File Size : 42,7 Mb
Release : 2012-04-30
Category : Science
ISBN : 9780486168784

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The Functions of Mathematical Physics by Harry Hochstadt Pdf

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.

Author : NIKIFOROV,UVAROV
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 50,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475715958

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Special Functions of Mathematical Physics by NIKIFOROV,UVAROV Pdf

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.

Author : Wilhelm Magnus
Publisher : Unknown
Page : 0 pages
File Size : 50,5 Mb
Release : 1966
Category : Mathematics
ISBN : OCLC:1110649840

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Formulas and Theorems for the Special Functions of Mathematical Physics by Wilhelm Magnus Pdf

Author : Wilhelm Magnus,Fritz Oberhettinger
Publisher : Unknown
Page : 194 pages
File Size : 47,9 Mb
Release : 1949
Category : Mathematics
ISBN : WISC:89083914481

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Formulas and Theorems for the Special Functions of Mathematical Physics, by Wilhelm Magnus and Fritz Oberhettinger ; Tr. from the German by John Werner by Wilhelm Magnus,Fritz Oberhettinger Pdf

Author : Hans J. Weber,George B. Arfken
Publisher : Academic Press
Page : 960 pages
File Size : 55,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780120598779

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Essential Mathematical Methods for Physicists, ISE by Hans J. Weber,George B. Arfken Pdf

This new adaptation of Arfken and Weber's best-selling Mathematical Methods for Physicists, fifth edition, is the most modern collection of mathematical principles for solving physics problems.

Author : Victor Henner,Tatyana Belozerova,Kyle Forinash
Publisher : CRC Press
Page : 859 pages
File Size : 54,7 Mb
Release : 2009-06-18
Category : Mathematics
ISBN : 9781439865163

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Mathematical Methods in Physics by Victor Henner,Tatyana Belozerova,Kyle Forinash Pdf

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

Author : A. S. Demidov
Publisher : Nova Publishers
Page : 154 pages
File Size : 47,5 Mb
Release : 2001
Category : Mathematics
ISBN : 1560729058

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Generalized Functions in Mathematical Physics by A. S. Demidov Pdf

This important book gives an interconnected presentation of some basic ideas, concepts, results of the theory of generalised functions (first of all, in the framework of the theory of distributions) and equations of mathematical physics. A part of the material is given according to the scheme: definition -- theorem -- proof. This scheme is convenient for presenting results in clear and concentrated form. However, it seems reasonable to give a student the possibility not only to study a priori given definitions and proofs of theorems, but also to discover them while considering the problems involved. A series of sections serve this purpose. Moreover, a part of the material is given as exercises and problems.

Author : Vasiliĭ I︠A︡kovlevich Arsenin
Publisher : Unknown
Page : 380 pages
File Size : 48,9 Mb
Release : 1968
Category : Science
ISBN : UOM:39015065694674

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Basic Equations and Special Functions of Mathematical Physics by Vasiliĭ I︠A︡kovlevich Arsenin Pdf

Author : Wilhelm Magnus,Fritz Oberhettinger
Publisher : Unknown
Page : 202 pages
File Size : 40,6 Mb
Release : 1954
Category : Functions
ISBN : UOM:39015017286504

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Formulas and Theorems for the Functions of Mathematical Physics by Wilhelm Magnus,Fritz Oberhettinger Pdf

Author : Sergeĭ I︠U︡rʹevich Slavi︠a︡nov,Wolfgang Lay
Publisher : Oxford University Press, USA
Page : 318 pages
File Size : 46,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0198505736

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Special Functions by Sergeĭ I︠U︡rʹevich Slavi︠a︡nov,Wolfgang Lay Pdf

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.

Author : Valeriya Akhmedova,Emil T. Akhmedov
Publisher : Springer Nature
Page : 116 pages
File Size : 51,5 Mb
Release : 2019-11-14
Category : Science
ISBN : 9783030350895

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Selected Special Functions for Fundamental Physics by Valeriya Akhmedova,Emil T. Akhmedov Pdf

This book presents calculation methods that are used in both mathematical and theoretical physics. These methods will allow readers to work with selected special functions and more generally with differential equations, which are the most frequently used in quantum mechanics, theory of relativity and quantum field theory. The authors explain various approximation methods used to solve differential equations and to estimate integrals. They also address the basics of the relations between differential equations, special functions and representation theory of some of the simplest algebras on the one hand, and fundamental physics on the other. Based on a seminar for graduate physics students, the book offers a compact and quick way to learn about special functions. To gain the most from it, readers should be familiar with the basics of calculus, linear algebra, and complex analysis, as well as the basic methods used to solve differential equations and calculate integrals.

Author : Richard Beals,Roderick Wong
Publisher : Cambridge University Press
Page : 128 pages
File Size : 40,5 Mb
Release : 2010-08-12
Category : Mathematics
ISBN : 9781139490436

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Special Functions by Richard Beals,Roderick Wong Pdf

The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

Author : Ian Naismith Sneddon
Publisher : Unknown
Page : 200 pages
File Size : 49,9 Mb
Release : 1961
Category : Functions
ISBN : UOM:39015053611391

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Special Functions of Mathematical Physics and Chemistry by Ian Naismith Sneddon Pdf