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Stieltjes transforms and the Stokes phenomenon. (English) Zbl 0704.33002
There is a recent interest in the so called Stokes phenomenon in asymptotic analysis which is initiated by 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 ν (z).
Reviewer: N.M.Temme

MSC:
33B20Incomplete beta and gamma functions
33C10Bessel and Airy functions, cylinder functions, 0 F 1
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
30E15Asymptotic representations in the complex domain