Special Functions

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

Publisher: Cambridge University Press

ISBN: 9780521789882

Category: Mathematics

Page: 664

View: 5041

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
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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: 8437

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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The Special Functions and Their Approximations

Author: Yudell L. Luke

Publisher: Academic Press

ISBN: 0080955606

Category: Mathematics

Page: 348

View: 5448

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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Vistas of Special Functions II

Author: Kalyan Chakraborty,Shigeru Kanemitsu,Haruo Tsukada

Publisher: World Scientific

ISBN: 981427397X

Category: Mathematics

Page: 272

View: 4865

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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Special Functions & Their Applications

Author: N. N. Lebedev

Publisher: Courier Corporation

ISBN: 0486139891

Category: Mathematics

Page: 308

View: 556

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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Special Functions

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

Publisher: World Scientific

ISBN: 9789971506674

Category: Mathematics

Page: 695

View: 5590

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

A Unified Theory Based on Singularities

Author: Wolfgang Lay

Publisher: Oxford University Press on Demand

ISBN: 9780198505730

Category: Mathematics

Page: 293

View: 7761

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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Asymptotics and Special Functions

Author: F. W. J. Olver

Publisher: Academic Press

ISBN: 148326744X

Category: Mathematics

Page: 588

View: 2800

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.
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Special Functions

Author: N.A

Publisher: Krishna Prakashan Media

ISBN: N.A

Category: Functions, Special

Page: 276

View: 3002

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Handbook of Special Functions

Derivatives, Integrals, Series and Other Formulas

Author: Yury A. Brychkov

Publisher: CRC Press

ISBN: 158488956X

Category: Mathematics

Page: 704

View: 6604

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 physics, engineering, and mathematics. The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of problems. It also discusses formulas of connection and conversion for elementary and special functions, such as hypergeometric and Meijer G functions.
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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: 5853

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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Special Functions of Mathematics for Engineers

Author: Larry C. Andrews

Publisher: SPIE Press

ISBN: 9780819426161

Category: Mathematics

Page: 479

View: 2453

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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Numerical Methods for Special Functions

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

Publisher: SIAM

ISBN: 0898716349

Category: Mathematics

Page: 415

View: 2578

An overview that advises when to use specific methods depending upon the function and range.
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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: 8803

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 2000: Current Perspective and Future Directions

current perspective and future directions : [proceedings of the NATO Advanced Study Institute on Special Functions 2000: Current Perspective and Future Directions, Tempe, Arizona, USA, 29 May-9 June 2000]

Author: Joaquin Bustoz,Mourad Ismail,Sergeĭ Konstantinovich Suslov

Publisher: Springer Science & Business Media

ISBN: 9780792371199

Category: Mathematics

Page: 520

View: 5207

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, Painleve classification.
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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: 563

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.
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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: 500

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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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: 3707

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: Group Theoretical Aspects and Applications

Author: R.A. Askey,Tom H. Koornwinder,Walter J. Schempp

Publisher: Springer Science & Business Media

ISBN: 9401097879

Category: Mathematics

Page: 352

View: 2279

Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
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