Handbook of Continued Fractions for Special Functions
Handbook of Continued Fractions for Special Functions

Author: Annie A.M. Cuyt

Publisher: Springer Science & Business Media

Published: 2008-04-12

Total Pages: 430

ISBN-13: 1402069499

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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!

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: 158488956X

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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 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.

Special Functions in Physics with MATLAB
Special Functions in Physics with MATLAB

Author: Wolfgang Schweizer

Publisher: Springer Nature

Published: 2021-03-25

Total Pages: 282

ISBN-13: 3030642321

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This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.

A Handbook of Generalized Special Functions for Statistical and Physical Sciences
A Handbook of Generalized Special Functions for Statistical and Physical Sciences

Author: A. M. Mathai

Publisher: Oxford University Press, USA

Published: 1993

Total Pages: 264

ISBN-13:

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Complicated generalized special functions such as Meijer's G-functions and functions of matrix arguments are here presented at a level suitable for every potential user. This handbook is thus a valuable reference source and a manual for researchers and advanced students in mathematical statistics, mathematical physics, several branches of mathematics, engineering problems, econometrics, and various applied areas where transcendental functions are used.

Handbook of Function and Generalized Function Transformations
Handbook of Function and Generalized Function Transformations

Author: Ahmed I. Zayed

Publisher: CRC Press

Published: 2019-08-21

Total Pages: 672

ISBN-13: 0429610912

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Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems. The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included. The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections:

Numerical Methods for Special Functions
Numerical Methods for Special Functions

Author: Amparo Gil

Publisher: SIAM

Published: 2007-01-01

Total Pages: 431

ISBN-13: 9780898717822

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Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an up-to-date overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. Not only are standard and simple parameter domains considered, but methods valid for large and complex parameters are described as well. The first part of the book (basic methods) covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions; however, it is suitable for general numerical courses. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions, Padé approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).

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.