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Zbl 0974.41021
Wong, R.; Zhao, Y.-Q.
Smoothing of Stokes's discontinuity for the generalized Bessel function. II.
(English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 455, No.1988, 3065-3084 (1999). ISSN 1364-5021; ISSN 1471-2946/e

[For part I see the authors in ibid. 455, No. 1984, 1381-1400 (1999).]\par The generalized Bessel function $\phi(z)=\sum_{n=0}^\infty z^n/[n! \Gamma(\rho n+\beta)]$, is usually defined for $0<\rho<\infty$ and $\beta$ real or complex. In an earlier paper the superasymptotics and hyperasymptotics of this functions is considered. In this second part the function is discussed for $-1<\rho<0$. Saddle point methods are used to derive the asymptotic expansion, with a detailed analysis of the saddle point contours, the Stokes lines and the smoothing of the Stokes discontinuity.
[N.M.Temme (Amsterdam)]
MSC 2000:
*41A60 Asymptotic problems in approximation
33C10 Cylinder functions, etc.

Keywords: asymptotic expansions; generalized Bessel functions; Stokes' phenomenon; hyperasymptotics

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