The Special Functions and Their Approximations

Author: Yudell L. Luke

Publisher: Academic Press

ISBN: 0080955606

Category: Mathematics

Page: 348

View: 7300

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

Author: Larry C. Andrews

Publisher: SPIE Press

ISBN: 9780819426161

Category: Mathematics

Page: 479

View: 8105

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

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: 1094

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

A Unified Theory Based on Singularities

Author: Wolfgang Lay

Publisher: Oxford University Press on Demand

ISBN: 9780198505730

Category: Mathematics

Page: 293

View: 3147

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.

Special Functions 2000: Current Perspective and Future Directions

Author: Joaquin Bustoz,Mourad E.H. Ismail,Sergei Suslov

Publisher: Springer Science & Business Media

ISBN: 9401008183

Category: Mathematics

Page: 520

View: 369

The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painlevé classification.

Special Functions & Their Applications

Author: N. N. Lebedev

Publisher: Courier Corporation

ISBN: 0486139891

Category: Mathematics

Page: 308

View: 8049

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.

Special Functions

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

Publisher: Cambridge University Press

ISBN: 9780521789882

Category: Mathematics

Page: 682

View: 1439

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

Special Functions

Author: N.A

Publisher: Krishna Prakashan Media


Category: Functions, Special

Page: 276

View: 7629


Special Functions

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

Publisher: World Scientific

ISBN: 9789971506674

Category: Mathematics

Page: 695

View: 4465

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

Vistas of Special Functions II

Author: Kalyan Chakraborty,Shigeru Kanemitsu,Haruo Tsukada

Publisher: World Scientific

ISBN: 981427397X

Category: Mathematics

Page: 272

View: 3774

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.

An Essay Toward a Unified Theory of Special Functions

Author: Clifford Truesdell

Publisher: Princeton University Press

ISBN: 9780691095776

Category: Mathematics

Page: 182

View: 3830

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

Proceedings of the International Workshop, Special Functions

Hong Kong, 21-25 June 1999

Author: Charles F. Dunkl,Mourad Ismail,Roderick Wong

Publisher: World Scientific

ISBN: 9789810243937

Category: Mathematics

Page: 438

View: 2676

Special functions and q-series are currently very active areas of research which overlap with many other areas of mathematics, such as representation theory, classical and quantum groups, affine Lie algebras, number theory, harmonic analysis, and mathematical physics. This book presents the state-of-the-art of the subject and its applications.

Special Functions: Fractional Calculus and the Pathway for Entropy

Author: Hans J. Haubold

Publisher: MDPI

ISBN: 3038426652


Page: 304

View: 9851

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

Special Functions of Mathematical (Geo-)Physics

Author: Willi Freeden,Martin Gutting

Publisher: Springer Science & Business Media

ISBN: 3034805632

Category: Mathematics

Page: 501

View: 1346

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.

Elements Of Ordinary Differential Equations And Special Functions

Author: A. Chakrabarty

Publisher: New Age International

ISBN: 9788122408805


Page: 168

View: 2325

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.

Numerical Methods for Special Functions

Author: Amparo Gil,Javier Segura,Nico M. Temme

Publisher: SIAM

ISBN: 0898716349

Category: Mathematics

Page: 415

View: 9203

An overview that advises when to use specific methods depending upon the function and range.

Orthogonal Polynomials and Special Functions

Author: Richard Askey

Publisher: SIAM

ISBN: 0898710189

Category: Mathematics

Page: 110

View: 8771

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

Asymptotics and Special Functions

Author: F. W. J. Olver

Publisher: Academic Press

ISBN: 148326744X

Category: Mathematics

Page: 588

View: 3990

Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.