Numerical Methods for Special Functions

Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. It considers not only standard and simple parameter domains, but also describes methods valid for large and complex parameters. While its focus is on the computation of special functions, it is also suitable for general numerical analysis courses. The authors provide pseudoalgorithms to help students write their own algorithms, and also discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions and Padé approximations. It also includes specific algorithms for computing several special functions. Intended for researchers in applied mathematics, scientific computing, physics, engineering, statistics, and other scientific disciplines in which special functions are used as computational tools.

Spis treści:
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.