Computation of Special Functions

Deals with the automatic computation of special functions which appear in all areas of engineering and the physical sciences. Contains over 100 computer programs written by the authors and describes the algorithms to provide readers with specific information about each individual program. Consisting of three sections, the first one presents an introduction to the special function to be dealt with, its major properties, and several formulas needed for its computation. The second segment features algorithms for computing the special function and the related quantities and lists corresponding Fortran-77 programs. The final part tabulates representative results to offer a quick outlook on the function's behavior and to check the computed results. The accompanying disk contains all the computer programs discussed in the text. The computation of special functions is a fundamental aspect of numerical analysis in virtually all areas of engineering and the physical sciences. Because most of these special functions are in the form of infinite series or infinite integrals, their solutions are often quite complicated. Fortunately, the difficulty has been lessened considerably by the advent of powerful personal computer hardware and software. Yet, until now, no single-source reference has offered comprehensive coverage of the automated computation of special functions.
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 programs' algorithms as well as specific information about each program's internal structure.
To facilitate quick reference, each chapter follows the same, three-part format. The first part covers major properties and important formulas needed for computation. The second part contains a description of the algorithm or algorithms at the heart of the FORTRAN-77 program in question. In the third part, the authors tabulate representative results to provide an at-a-glance understanding of the function's behavior as well as a valuable data-check for their computed results.
Computation of Special Functions is an indispensable tool for engineers and physical scientists as well as for students involved in advanced research in these fields.
An indispensable tool for anyone who needs to compute solutions for special functions
Computation of Special Functions is devoted exclusively to the automated solution of special functions used in all areas of engineering and the physical sciences. Not just another collection of formulas, graphs, and tables for special functions, this powerful book/software package:
Treats most special functions used in numerical analysis in the physical sciences
Covers functions usually not found in most software packages
Supplies more than 100 original programs for computing special functions
Describes the underlying algorithm or algorithms for each program
Provides valuable information on each program's internal structure and development
Offers a wealth of examples of typical computational results

List of contents

Bernoulli and Euler Numbers.
Orthogonal Polynomials.
Gamma, Beta, and Psi Functions.
Legendre Functions.
Bessel Functions.
Modified Bessel Functions.
Integrals of Bessel Functions.
Spherical Bessel Functions.
Kelvin Functions.
Airy Functions.
Struve Functions.
Hypergeometric and Confluent Hypergeometric Functions.
Parabolic Cylinder Functions.
Mathieu Functions.
Spheroidal Wave Functions.
Error Function and Fresnel Integrals.
Cosine and Sine Integrals.
Elliptic Integrals and Jacobian Elliptic Functions.
Exponential Integrals.
Summary of Methods for Computing Special Functions.
Appendices.
Indexes.

About the author

JIANMING JIN, PhD, earned his doctorate in electrical engineering at the University of Michigan and is currently a professor at the University of Illinois. He is the author of the first edition of The Finite Element Method in Electromagnetics, Computation of Special Functions (with S. Zhang; published by Wiley), Electromagnetic Analysis and Design in Magnetic Resonance Imaging, and coedited (with W. C. Chew, E. Michielssen, and J. M. Song) Fast and Efficient Algorithms in Computational Electromagnetics.§

Product details

• Authors: Jianming Jin, Shanjie Zhang
• Publisher: Wiley & Sons
• Languages: English
• Product format: Hardback
• Released: 01.01.1996
• EAN: 9780471119630
• ISBN: 978-0-471-11963-0
• No. of pages: 718
• Dimensions: 166 mm x 243 mm x 43 mm
• Weight: 1276 g
• Subject: Natural sciences, medicine, IT, technology > Technology > Electronics, electrical engineering, communications engineering