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9780898716344 Academic Inspection Copy

Numerical Methods for Special Functions

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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).
Amparo Gil is an Associate Professor of Applied Mathematics at the Universidad de Cantabria in Spain. Javier Segura is an Associate Professor of Mathematical Analysis at the Universidad de Cantabria in Spain. Nico M. Temme is a guest researcher at the 'Centrum voor Wiskunde en Informatica' (CWI) in Amsterdam, since his retirement in 2005.
List of Algorithms Preface Chapter 1: Introduction Part I: Basic Methods. 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.
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