# Numerical Methods for Special Functions

## Amparo Gil; Javier Segura; Nico M. Temme

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Special functions arise in many problems of pure and applied mathematics, statistics, physics, and engineering. This book provides an up-to-date overview of methods for computing special functions and discusses when to use them in standard parameter domains, as well as in large and complex domains.

The first part of the book covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss 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 (Airy functions and parabolic cylinder functions, among others).

Audience: 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.

Contents: 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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Book Description:

An overview of numerical methods for computing special functions, which 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.

About the Author:

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.

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## 1.Numerical Methods for Special Functions (Paperback)

Editorial: Society for Industrial Applied Mathematics,U.S., United States (2008)
ISBN 10: 0898716349 ISBN 13: 9780898716344
Nuevos Paperback Cantidad: 1
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Descripción Society for Industrial Applied Mathematics,U.S., United States, 2008. Paperback. Estado de conservación: New. Language: English . Brand New Book. 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 Pade 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. Nº de ref. de la librería AAN9780898716344

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## 2.Numerical Methods for Special Functions

Editorial: Society for Industrial and Applied Mathematics (2008)
ISBN 10: 0898716349 ISBN 13: 9780898716344
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Descripción Society for Industrial and Applied Mathematics, 2008. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería CE-9780898716344

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## 3.Numerical Methods for Special Functions (Paperback)

Editorial: Society for Industrial Applied Mathematics,U.S., United States (2008)
ISBN 10: 0898716349 ISBN 13: 9780898716344
Nuevos Paperback Cantidad: 1
Librería
The Book Depository US
(London, Reino Unido)
Valoración

Descripción Society for Industrial Applied Mathematics,U.S., United States, 2008. Paperback. Estado de conservación: New. Language: English . Brand New Book. 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 Pade 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. Nº de ref. de la librería AAN9780898716344

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## 4.Numerical Methods for Special Functions

Editorial: Society for Industrial & Applied Mathematics,U.S.
ISBN 10: 0898716349 ISBN 13: 9780898716344
Nuevos Paperback Cantidad: 1
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Descripción Society for Industrial & Applied Mathematics,U.S. Paperback. Estado de conservación: new. BRAND NEW, Numerical Methods for Special Functions, Amparo Gil, Javier Segura, Nico M. Temme, 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 Pade 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. Nº de ref. de la librería B9780898716344

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## 5.Numerical Methods for Special Functions

Editorial: Society for Industrial Mathematics (2007)
ISBN 10: 0898716349 ISBN 13: 9780898716344
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Descripción Society for Industrial Mathematics, 2007. Paperback. Estado de conservación: New. 1. Nº de ref. de la librería DADAX0898716349

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## 6.Numerical Methods for Special Functions

Editorial: Cambridge Univ Pr (2008)
ISBN 10: 0898716349 ISBN 13: 9780898716344
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Descripción Cambridge Univ Pr, 2008. Paperback. Estado de conservación: Brand New. 1st edition. 430 pages. 9.90x6.90x0.70 inches. In Stock. Nº de ref. de la librería __0898716349

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## 7.Numerical Methods for Special Functions

Editorial: Society for Industrial Mathem (2007)
ISBN 10: 0898716349 ISBN 13: 9780898716344
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Descripción Society for Industrial Mathem, 2007. Paperback. Estado de conservación: New. Never used!. Nº de ref. de la librería P110898716349

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## 8.Numerical Methods for Special Functions

Editorial: Society for Industrial Mathematics (2007)
ISBN 10: 0898716349 ISBN 13: 9780898716344
Nuevos Paperback Cantidad: 1
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Ergodebooks
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Descripción Society for Industrial Mathematics, 2007. Paperback. Estado de conservación: New. Nº de ref. de la librería SONG0898716349

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