Special Functions

Special Functions
Author: George E. Andrews
Publisher: Cambridge University Press
Total Pages: 684
Release: 1999
Genre: Mathematics
ISBN: 9780521789882

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

Special Functions

Special Functions
Author: Nico M. Temme
Publisher: John Wiley & Sons
Total Pages: 392
Release: 2011-03-01
Genre: Mathematics
ISBN: 1118030818

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 for Applied Scientists

Special Functions for Applied Scientists
Author: A.M. Mathai
Publisher: Springer Science & Business Media
Total Pages: 480
Release: 2008-02-13
Genre: Science
ISBN: 0387758941

This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.

Special Functions in Physics with MATLAB

Special Functions in Physics with MATLAB
Author: Wolfgang Schweizer
Publisher: Springer Nature
Total Pages: 282
Release: 2021-03-25
Genre: Science
ISBN: 3030642321

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.

Special Functions of Mathematical Physics

Special Functions of Mathematical Physics
Author: NIKIFOROV
Publisher: Springer Science & Business Media
Total Pages: 443
Release: 2013-11-11
Genre: Mathematics
ISBN: 1475715951

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: Z. X. Wang
Publisher: World Scientific
Total Pages: 720
Release: 1989
Genre: Mathematics
ISBN: 9789971506674

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

Computation of Special Functions

Computation of Special Functions
Author: Shanjie Zhang
Publisher: Wiley-Interscience
Total Pages: 752
Release: 1996-07-26
Genre: Computers
ISBN:

Computation of Special Functions is a valuable book/software package containing more than 100 original computer programs for the computation of most special functions currently in use. These include many functions commonly omitted from available software packages, such as the Bessel and modified Bessel functions, the Mathieu and modified Mathieu functions, parabolic cylinder functions, and various prolate and oblate spheroidal wave functions. Also, unlike most software packages, this book/disk set gives readers the latitude to modify programs according to the special demands of the sophisticated problems they are working on. The authors provide detailed descriptions of the program's algorithms as well as specific information about each program's internal structure.

Special Functions for Scientists and Engineers

Special Functions for Scientists and Engineers
Author: W. W. Bell
Publisher: Courier Corporation
Total Pages: 274
Release: 2013-07-24
Genre: Technology & Engineering
ISBN: 0486317560

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.

Numerical Methods for Special Functions

Numerical Methods for Special Functions
Author: Amparo Gil
Publisher: SIAM
Total Pages: 431
Release: 2007-01-01
Genre: Mathematics
ISBN: 9780898717822

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).