Uniform asymptotic expansions of integrals: A selection of problems

[摘要] On the occasion of the conference we mention examples of Stieltjes' work on asymptotics of special functions. The remaining part of the paper gives. 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.

[发布日期] 1995-12-29

[效力级别]  Proceedings Paper

[关键词] uniform asymptotic expansion;error function;incomplete gamma functions;Stirling numbers;Fermi-Dirac integral;statistical distribution functions;Stokes phenomenon