Cover image for Numerical methods for special functions
Title:
Numerical methods for special functions
Personal Author:
Publication Information:
Philadelphia : Society for Industrial Mathematics, 2007
Physical Description:
xiv, 417 p. : ill. ; 26 cm.
ISBN:
9780898716344

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PSZ JB 30000010178734 QA351 G54 2007 Open Access Book
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PSZ KL 30000010193722 QA351 G54 2007 Open Access Book Book
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Summary

Summary

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, Pad#65533; approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).


Table of Contents

List of algorithms
Preface
1 Introduction
Part I Basic Methods
2 Convergent and divergent series
3 Chebyshev expansions
4 Recurrence relations and continued fractions
5 Quadrature methods
Part II Further Tools and Methods
6 Continued fractions
7 Computation of the zeros of special functions
8 Uniform asymptotic expansions
9 Other methods
Part III Related Topics and Examples
10 Inversion of distribution functions
11 Further examples
Part IV Software
12 Associated algorithms
Bibliography
Index