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Full Description
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, Pade approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).
Contents
* List of Algorithms* Preface* Chapter 1Methods. Chapter 2: Convergent and Divergent Series* Chapter 3: Chebyshev Expansions* Chapter 4: Linear Recurrence Relations and Associated Continued Fractions* Chapter 5: Quadrature Methods* Part II: Further Tools and Methods. Chapter 6: Numerical Aspects of Continued Fractions* Chapter 7: Computation of the Zeros of Special Functions* Chapter 8: Uniform Asymptotic Expansions* Chapter 9: Other Methods* Part III: Related Topics and Examples. Chapter 10: Inversion of Cumulative Distribution Functions* Chapter 11: Further Examples* Part IV: Software. Chapter 12: Associated Algorithms* Bibliography* Index.
