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Numerical methods for special functions [electronic resource] /

Amparo Gil, Javier Segura, Nico M. Temme.

Book Cover
Main Author: Gil, Amparo.
Other Names: Segura, Javier. | Temme, N. M.
Published: Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2007.
Topics: Functions, Special - Data processing. | Numerical analysis. | Asymptotic expansions. | Approximation theory.
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100 1 |aGil, Amparo.
245 10|aNumerical methods for special functions|h[electronic resource] /|cAmparo Gil, Javier Segura, Nico M. Temme.
260 |aPhiladelphia, Pa. :|bSociety for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),|c2007.
300 |a1 electronic text (xiv, 417 p. : ill.) :|bdigital file.
504 |aIncludes bibliographical references (p. 389-404) and index.
505 0 |aPreface -- 1. Introduction -- I. Basic methods -- 2. Convergent and divergent series -- 3. Chebyshev expansions -- 4. Linear recurrence relations and associated continued fractions -- 5. Quadrature methods -- II. Further tools and methods -- 6. Numerical aspects of continued fractions -- 7. Computation of the zeros of special functions -- 8. Uniform asymptotic expansions -- 9. Other methods -- III. Related topics and examples -- 10. Inversion of cumulative distribution functions -- 11. Further examples -- 12. Associated algorithms -- List of algorithms -- Bibliography -- Index.
506 |aRestricted to subscribers or individual electronic text purchasers.
520 3 |aSpecial 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, Padâe approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).
530 |aAlso available in print version.
538 |aMode of access: World Wide Web.
538 |aSystem requirements: Adobe Acrobat Reader.
588 |aTitle from title screen, viewed 10/20/2010.
588 |aDescription based on title page of print version.
650 0|aFunctions, Special|xData processing.
650 0|aNumerical analysis.
650 0|aAsymptotic expansions.
650 0|aApproximation theory.
653 |aComputation of special functions
653 |aChebyshev expansions
653 |aNumerical quadrature
653 |aRecurrence relations and continued fractions
653 |aAsymptotic analysis
653 |aZeros of special functions
700 1 |aSegura, Javier.
700 1 |aTemme, N. M.
710 2 |aSociety for Industrial and Applied Mathematics.
776 08|iPrint version:|z0898716349|z9780898716344|w(DLC) 2007061738
856 40|3SIAM|u|zAccess to the electronic version for current IIT main & branch campus students, faculty, & staff

Staff View for: Numerical methods for special functions