Special Functions

An Introduction to the Classical Functions of Mathematical Physics

Author: Nico M. Temme

Publisher: John Wiley & Sons

ISBN: 1118030818

Category: Mathematics

Page: 392

View: 2848

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.
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Special Functions

Author: George E. Andrews,Richard Askey,Ranjan Roy

Publisher: Cambridge University Press

ISBN: 9780521789882

Category: Mathematics

Page: 682

View: 4162

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
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The Special Functions and Their Approximations

Author: Yudell L. Luke

Publisher: Academic Press

ISBN: 0080955606

Category: Mathematics

Page: 348

View: 4278

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.
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Special Functions of Mathematics for Engineers

Author: Larry C. Andrews

Publisher: SPIE Press

ISBN: 9780819426161

Category: Mathematics

Page: 479

View: 6474

Designed to serve as a classroom text for higher mathematical functions and a reference text for engineers and scientists, presents applications from such fields as statics, dynamics, statistical communication theory, fiber optics, heat conduction in solids, hybridation phenomena, and fluid mechanic
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Special Functions

Author: Z. X. Wang,D. R. Guo

Publisher: World Scientific

ISBN: 9789971506674

Category: Mathematics

Page: 695

View: 3370

Contains the various principal special functions in common use and their basic properties and manipulations. Discusses expansions of functions in infinite series and infinite product and the asymptotic expansion of functions. For physicists, engineers, and mathematicians. Acidic paper. Paper edition (unseen), $38. Annotation copyrighted by Book News, Inc., Portland, OR
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Special Functions

Author: N.A

Publisher: Krishna Prakashan Media

ISBN: N.A

Category: Functions, Special

Page: 276

View: 1091

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Special Functions

A Unified Theory Based on Singularities

Author: Wolfgang Lay

Publisher: Oxford University Press on Demand

ISBN: 9780198505730

Category: Mathematics

Page: 293

View: 6435

The topic of special functions, normally presented as a mere collection of functions exhibiting particular properties, is treated from a fresh and unusual perspective in this book. The authors have based the special functions on the theory of second-order ordinary differential equations in the complex domain. Several physical applications are presented. Numerous tables and figures will help the reader find his way through the subject.
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Special Functions for Scientists and Engineers

Author: W. W. Bell

Publisher: Courier Corporation

ISBN: 0486317560

Category: Technology & Engineering

Page: 272

View: 4428

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.
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Special Functions & Their Applications

Author: N. N. Lebedev

Publisher: Courier Corporation

ISBN: 0486139891

Category: Mathematics

Page: 308

View: 3385

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.
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Vistas of Special Functions II

Author: Kalyan Chakraborty,Shigeru Kanemitsu,Haruo Tsukada

Publisher: World Scientific

ISBN: 981427397X

Category: Mathematics

Page: 272

View: 5198

This book (Vistas II), is a sequel to Vistas of Special Functions (World Scientific, 2007), in which the authors made a unification of several formulas scattered around the relevant literature under the guiding principle of viewing them as manifestations of the functional equations of associated zeta-functions. In Vista II, which maintains the spirit of the theory of special functions through zeta-functions, the authors base their theory on a theorem which gives some arithmetical Fourier series as intermediate modular relations ? avatars of the functional equations. Vista II gives an organic and elucidating presentation of the situations where special functions can be effectively used. Vista II will provide the reader ample opportunity to find suitable formulas and the means to apply them to practical problems for actual research. It can even be used during tutorials for paper writing.
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Elements Of Ordinary Differential Equations And Special Functions

Author: A. Chakrabarty

Publisher: New Age International

ISBN: 9788122408805

Category:

Page: 168

View: 7693

Ordinary Differential Equations And Special Functions Form A Central Part In Many Branches Of Physics And Engineering. A Large Number Of Books Already Exist In These Areas And Informations Are Therefore Available In A Scattered Form. The Present Book Tries To Bring Out Some Of The Most Important Concepts Associated With Linear Ordinary Differential Equations And The Special Functions Of Frequent Occurrence, In A Rather Elementary Form.The Methods Of Obtaining Series Solution Of Second Order Linear Ordinary Differential Equations Near An Ordinary Point As Well As Near A Regular Singular Point Have Been Explained In An Elegant Manner And, As Applications Of These Methods, The Special Functions Of Hermite And Bessel Have Been Dealt With.The Special Functions Of Legendre And Laguerre Have Also Been Discussed Briefly. An Appendix Is Prepared To Deal With Other Special Functions Such As The Beta Function, The Gamma Function, The Hypergeometric Functions And The Chebyshev Polynomials In A Short Form.The Topics Involving The Existence Theory And The Eigenvalue Problems Have Also Been Discussed In The Book To Create Motivation For Further Studies In The Subject.Each Chapter Is Supplemented With A Number Of Worked Out Examples As Well As A Number Of Problems To Be Handled For Better Understanding Of The Subject. R Contains A List Of Sixteen Important Books Forming The Bibliography.In This Second Edition The Text Has Been Thoroughly Revised.
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Handbook of Continued Fractions for Special Functions

Author: Annie A.M. Cuyt,Vigdis Petersen,Brigitte Verdonk,Haakon Waadeland,William B. Jones

Publisher: Springer Science & Business Media

ISBN: 9781402069499

Category: Mathematics

Page: 431

View: 4120

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!
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Special Functions: Fractional Calculus and the Pathway for Entropy

Author: Hans J. Haubold

Publisher: MDPI

ISBN: 3038426652

Category:

Page: 304

View: 4617

This book is a printed edition of the Special Issue "Special Functions: Fractional Calculus and the Pathway for Entropy Dedicated to Professor Dr. A.M. Mathai on the occasion of his 80th Birthday" that was published in Axioms
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An Essay Toward a Unified Theory of Special Functions

Author: Clifford Truesdell

Publisher: Princeton University Press

ISBN: 9780691095776

Category: Mathematics

Page: 182

View: 2564

The description for this book, An Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18, will be forthcoming.
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Orthogonal Polynomials and Special Functions

Author: Richard Askey

Publisher: SIAM

ISBN: 0898710189

Category: Mathematics

Page: 110

View: 7818

This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.
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Lie Theory and Special Functions

Author: Miller

Publisher: Academic Press

ISBN: 0080955517

Category: Mathematics

Page: 337

View: 6320

Lie Theory and Special Functions
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Special Functions of Mathematical (Geo-)Physics

Author: Willi Freeden,Martin Gutting

Publisher: Springer Science & Business Media

ISBN: 3034805632

Category: Mathematics

Page: 501

View: 9389

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.
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Special Functions

Author: Z X Wang,D R Guo

Publisher: World Scientific

ISBN: 9814507539

Category:

Page: 720

View: 1065

In this book, expansions of functions in infinite series and infinite product and the asymptotic expansion of functions are discussed. This may be the best reference book on Special Functions. Contents: The Expansion of Functions in Infinite Series and Infinite ProductsLinear Ordinary Differential Equations of the Second OrderThe Gamma FunctionHypergeometric FunctionLegendre FunctionsConfluent Hypergeometric FunctionsBessel FunctionsWeierstrass Elliptic FunctionsTheta FunctionsJacobian Elliptic FunctionsLamé Functions and Mathieu Functions Readership: Mathematicians, physicists and engineers. Keywords:Special Functions;Aymptotic Expansion;Functions in Infinite Series;Linear Ordinary Differential Equations of the Second Order;Gamma Function;Hypergeometric Function;Legendre Functions;Confluent Hypergeometric Functions;Bessel Functions;Weierstrass Elliptic Functions;Theta Functions;Jacobian Elliptic Functions;Lame Functions;Mathieu FunctionsReview: "In January 1980 when I visited Beijing, Professor Z X Wang, my MSc thesis advisor of many years ago, gave me a copy of his book with Mr D R Guo on Special Functions. On many occasions in the later years, I had consulted the book for various things such as the hypergeometric series and the elliptic functions. The book is systematic, clear and to the point, as one would expect from Professor Wang's style and personality. It is great news that the book is now being published in an English translation. It will benefit many students and research workers who do not read Chinese. " Foreword by C N Yang Nobel Laureate “This is quite a comprehensive treatise on special functions … This book should very well serve as a reference book for the topics listed above.” Monatshefte fur Mathematik “The book is a welcome addition to the classical works on special functions. The presentation is very clear. The great variety of topics makes it a useful and instructive source of information for many workers in physics, engineering and applied mathematics.” Mathematics Abstracts
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Special Functions, KZ Type Equations, and Representation Theory

Author: Aleksandr Nikolaevich Varchenko

Publisher: American Mathematical Soc.

ISBN: 0821828673

Category: Science

Page: 118

View: 7818

The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its $q$-deformations. In the book, the author discusses the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions. This book aims to provide an introduction to the area and expose different facets of the subject. It contains constructions, discussions of notions, statements of main results, and illustrative examples. The exposition is restricted to the simplest case of the theory associated with the Lie algebra $\mathfrak {sl}_2$. This book is intended for researchers and graduate students in mathematics and in mathematical physics, in particular to those interested in applications of special functions.
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