Asymptotic Methods for Integrals by Nico M Temme
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About this book :-
Asymptotic Methods for Integrals written 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.
In this book the classical methods that are available for one-dimensional integrals are described: integrating by parts, the method of stationary phase, and the saddle point method and the related method of steepest descent. For two- and higherdimensional integrals such methods are also available, and incidentally some of their elements are mentioned, but a more extensive treatment falls outside the scope of this book.
Integrals with large parameters occur in many problems from physics and statistics, and in particular they show up in the area of the classical functions of mathematical physics and probability theory, from which class many examples are taken to explain the classical methods.
Book Detail :-
Title: Asymptotic Methods for Integrals
Author(s): Nico M. Temme
Publisher: World Scientific Publishing Company
Series: Series in Analysis
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About Author :-
The author Nico M. Temme , Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands.
Nico Temme’s main research interests are the asymptotic and numerical aspects of special functions. He has published numerous papers on these topics, and his well-known book Special Functions: An Introduction to the Classical Functions of Mathematical Physics
Temme was a member of the original editorial committee for the DLMF project, in existence from the mid-1990’s to the mid-2010’s. During this time he served as Associate Editor with responsibilities for all aspects of the project.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF Special Functions: Classical Functions of Mathematical Physics by Nico M. Temme
• Download PDF Numerical Methods for Special Functions by Amparo Gil, Javier Segura, Nico Temme
• Download PDF Asymptotic Methods for Integrals by Nico M Temme
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Book Contents :-
Special Functions: Classical Functions of Mathematical Physics written by
Nico M. Temme
cover the following topics.
PART-1 Basic Methods for Integrals
2. Expansions of Laplace-type integrals: Watson’s lemma
3. The method of Laplace
4. The saddle point method and paths of steepest descent
5. The Stokes phenomenon
PART-2 Basic Methods: Examples for Special Functions
6. The gamma function
7. Incomplete gamma functions
8. The Airy functions
9. Bessel functions: Large argument
10. Kummer functions
11. Parabolic cylinder functions: Large argument
12. The Gauss hypergeometric function
13. Examples of 3F2-polynomials
PART-3 Other Methods for Integrals
14. The method of stationary phase
15. Coefficients of a power series. Darboux’s method
16. Mellin–Barnes integrals and Mellin convolution integrals
17. Alternative expansions of Laplace-type integrals
18. Two-point Taylor expansions
19. Hermite polynomials as limits of other classical orthogonal polynomials
PART-4 Uniform Methods for Integrals
20. An overview of standard forms
21. A saddle point near a pole
22. Saddle point near algebraic singularity
23. Two coalescing saddle points: Airy-type expansions
24. Hermite-type expansions of integrals
PART-5 Uniform Methods for Laplace-Type Integrals
25. The vanishing saddle point
26. A moving endpoint: Incomplete Laplace integrals
27. An essential singularity: Bessel-type expansions
28. Expansions in terms of Kummer functions
PART-6 Uniform Examples for Special Functions
29. Legendre functions
30. Parabolic cylinder functions: Large parameter
31. Coulomb wave functions
32. Laguerre polynomials: Uniform expansions
33. Generalized Bessel polynomials
34. Stirling numbers
35. Asymptotics of the integral
PART-7 A Class of Cumulative Distribution Functions
36. Expansions of a class of cumulative distribution functions
37. Incomplete gamma functions: Uniform expansions
38. Incomplete beta function
39. Non-central chi-square, Marcum functions
40. A weighted sum of exponentials
41. A generalized incomplete gamma function
42. Asymptotic inversion of cumulative distribution functions
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