Nico M. Temme's Books

Asymptotic Methods For Integrals

By: Nico M Temme

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Asymptotic Methods For Integrals

By: Nico M Temme

This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals.The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.

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Page Count

628

Publisher

World Scientific

Published Date

ISBN 10

9814612170

ISBN 13

9789814612173

Numerical Methods for Special Functions

By: Amparo Gil,Javier Segura,Nico M. Temme

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Numerical Methods for Special Functions

By: 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 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, Padé approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).

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Page Count

431

Publisher

SIAM

Published Date

ISBN 10

0898717825

ISBN 13

9780898717822

Special Functions

An Introduction to the Classical Functions of Mathematical Physics

By: Nico M. Temme

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Special Functions

An Introduction to the Classical Functions of Mathematical Physics

By: Nico M. Temme

This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.

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Page Count

392

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118030818

ISBN 13

9781118030813

Book's by Nico M. Temme

Asymptotic Methods For Integrals

Asymptotic Methods For Integrals

Numerical Methods for Special Functions

Numerical Methods for Special Functions

Special Functions

Special Functions

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