Formulas and Theorems for the Special Functions of Mathematical Physics

Formulas and Theorems for the Special Functions of Mathematical Physics

Author: Wilhelm Magnus

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 516

ISBN-13: 3662117614

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 Much of the material (part of it unpublished) did not appear in the earlier editions.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


Essential Mathematical Methods for Physicists, ISE

Essential Mathematical Methods for Physicists, ISE

Author: Hans J. Weber

Publisher: Academic Press

Published: 2004

Total Pages: 960

ISBN-13: 0120598779

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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.


Special Functions of Mathematical Physics

Special Functions of Mathematical Physics

Author: NIKIFOROV

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 443

ISBN-13: 1475715951

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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.


Special Functions

Special Functions

Author: Richard Beals

Publisher: Cambridge University Press

Published: 2010-08-12

Total Pages:

ISBN-13: 1139490435

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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.


Special Functions of Mathematical (Geo-)Physics

Special Functions of Mathematical (Geo-)Physics

Author: Willi Freeden

Publisher: Springer Science & Business Media

Published: 2013-02-15

Total Pages: 505

ISBN-13: 3034805632

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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

Special Functions

Author: George E. Andrews

Publisher: Cambridge University Press

Published: 1999

Total Pages: 684

ISBN-13: 9780521789882

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An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.


Handbook of Mathematical Functions

Handbook of Mathematical Functions

Author: Milton Abramowitz

Publisher: Courier Corporation

Published: 1965-01-01

Total Pages: 1068

ISBN-13: 9780486612720

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An extensive summary of mathematical functions that occur in physical and engineering problems


Handbook of Special Functions

Handbook of Special Functions

Author: Yury A. Brychkov

Publisher: CRC Press

Published: 2008-05-28

Total Pages: 702

ISBN-13: 1584889578

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Because of the numerous applications involved in this field, the theory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. The Handbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in


The Special Functions and Their Approximations

The Special Functions and Their Approximations

Author: Yudell L. Luke

Publisher: Academic Press

Published: 1969

Total Pages: 373

ISBN-13: 0080955606

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A detailed and self-contained and unified treatment of many mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. many common features of the Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, as well as of otherw, can be derived. Hitherto, many of the material upon which the volumes are based has been available only in papers scattered throughout the literature.


Special Functions of Mathematics for Engineers

Special Functions of Mathematics for Engineers

Author: Larry C. Andrews

Publisher: SPIE Press

Published: 1998

Total Pages: 512

ISBN-13: 9780819426161

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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.