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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
** Edition: **
** Author(s): ** Nico M. Temme
** Publisher: ** World Scientific Publishing Company
** Series: ** Series in Analysis
** Year: ** 2015
** Pages: ** 587
** Type: ** PDF
** Language: ** English
** ISBN: ** 9814612154,9789814612159,9781322501130,1322501130
** Country: ** Netherlands

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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

1. Introduction

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

Bibliography

Index

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