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Zbl 0849.41024
Temme, N.M.
Uniform asymptotic expansions of integrals: A selection of problems. (English)
[J] J. Comput. Appl. Math. 65, No.1-3, 395-417 (1995). ISSN 0377-0427

Summary: On the occasion of the conference we mention examples of Stieltjes' work on asymptotics of special functions. The remaining part of the paper gives a selection of asymptotic methods for integrals, in particular on uniform approximations. We discuss several ``standard'' problems and examples, in which known special functions (error functions, Airy functions, Bessel functions, etc.) are needed to construct uniform approximations. Finally, we discuss the recent interest and new insights in the Stokes phenomenon. An extensive bibliography on uniform asymptotic methods for integrals is given, together with references to recent papers on the Stokes phenomenon for integrals and related topics.

MSC 2000:: *41A60 Asymptotic problems in approximation
33B20 Incomplete beta and gamma functions
33C10 Cylinder functions, etc.
33C45 Orthogonal polynomials and functions of hypergeometric type
11B73 Bell and Stirling numbers
30E15 Asymptotic representations in the complex domain

Keywords: error functions; incomplete gamma functions; Stirling numbers; Fermi-Dirac integral; statistical distribution functions; Airy functions; Bessel functions; Stokes phenomenon; uniform asymptotic methods

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