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Zbl 0704.33002
Boyd, W.G.C.
Stieltjes transforms and the Stokes phenomenon. (English)
[J] Proc. R. Soc. Lond., Ser. A 429, No.1876, 227-246 (1990). ISSN 0080-4630

There is a recent interest in the so called Stokes phenomenon in asymptotic analysis which is initiated by {\it M. V. Berry} in his paper in Proc. R. Soc. Lond., Ser. A 422, No.1862, 7-21 (1989; Zbl 0683.33004)]. In the new interpretation of the phenomenon, an error function is introduced to describe the rapid change in the behaviour of the remainders as a Stokes line is crossed. The present paper describes how Stieltjes transforms can be used for investigating this problem for instance for the Bessel function $K\sb{\nu}(z)$.
[N.M.Temme]

MSC 2000:: *33B20 Incomplete beta and gamma functions
33C10 Cylinder functions, etc.
41A60 Asymptotic problems in approximation
30E15 Asymptotic representations in the complex domain

Keywords: Stokes phenomenon; error function; Stieltjes transforms; Bessel function

Citations: Zbl 0683.33004

Cited in: Zbl 0772.33015

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