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Formulas and Theorems for the Special Functions of Mathematical Physics

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Release : 2013-11-11
Genre : Science
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Book Synopsis Formulas and Theorems for the Special Functions of Mathematical Physics by : Wilhelm Magnus

Download or read book Formulas and Theorems for the Special Functions of Mathematical Physics written by Wilhelm Magnus. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: 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 Much of the material (part of it unpublished) did not appear in the earlier editions.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.

Formulas and Theorems for the Special Functions of Mathematical Physics Special Functions of Mathematical Physics

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Release : 1966
Genre :
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Book Synopsis Formulas and Theorems for the Special Functions of Mathematical Physics Special Functions of Mathematical Physics by : Ronald Gross

Download or read book Formulas and Theorems for the Special Functions of Mathematical Physics Special Functions of Mathematical Physics written by Ronald Gross. This book was released on 1966. Available in PDF, EPUB and Kindle. Book excerpt:

The Functions of Mathematical Physics

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Release : 2012-04-30
Genre : Science
Kind : eBook
Book Rating : 786/5 ( reviews)

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Book Synopsis The Functions of Mathematical Physics by : Harry Hochstadt

Download or read book The Functions of Mathematical Physics written by Harry Hochstadt. This book was released on 2012-04-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Formulas and theorems forthe special functions of mathematical physics

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Author :
Release : 1966
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Kind : eBook
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Book Synopsis Formulas and theorems forthe special functions of mathematical physics by :

Download or read book Formulas and theorems forthe special functions of mathematical physics written by . This book was released on 1966. Available in PDF, EPUB and Kindle. Book excerpt:

Special Functions of Mathematical Physics

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Author :
Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 951/5 ( reviews)

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Book Synopsis Special Functions of Mathematical Physics by : NIKIFOROV

Download or read book Special Functions of Mathematical Physics written by NIKIFOROV. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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