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Numerical Methods for Special FunctionsNumerical Methods for Special Functions

Amparo Gil, Javier Segura, and Nico M. Temme

“This book is inventive and original—an exceedingly valuable collection of methods to compute special functions, bringing together material usually found only in disparate sources.”
—Van Snyder, Jet Propulsion Laboratory, California Institute of Technology.

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).

This book is intended for researchers in applied mathematics, scientific computing, physics, engineering, statistics, and other scientific disciplines in which special functions are used as computational tools. Some chapters can be used in general numerical analysis courses.

Table of Contents

About the Authors
Amparo Gil is an Associate Professor of Applied Mathematics at Universidad de Cantabria (Spain). Her main research interests are in numerical analysis, with special emphasis on numerical methods and software for the computation of special functions.

Javier Segura is an Associate Professor of Mathematical Analysis at Universidad de Cantabria (Spain). His research focuses on numerical analysis and, in particular, the computation of special functions and numerical software.

Since his retirement from CWI in Amsterdam, Nico M. Temme has been a guest researcher at CWI. He has served as editor for a number of scientific journals, is the author of Special Functions: An Introduction to the Classical Functions of Mathematical Physics (Wiley, 1996), and wrote four chapters for the Digital Library of Mathematical Functions, the replacement for the Handbook of Mathematical Functions (Abramowitz and Stegun, 1964). He also serves on the editorial board for this project. His research interest is asymptotic analysis and the numerical evaluation of special functions.

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2007 / xvi + 415 pages / Softcover / ISBN 978-0-898716-34-4
List Price $105.50 / SIAM Member Price $73.85 / Order Code OT99
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