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Zbl 0729.33002
Berry, M.V.
Infinitely many Stokes smoothings in the gamma function. (English)
[J] Proc. R. Soc. Lond., Ser. A 434, No.1891, 465-472 (1991). ISSN 0080-4630

Stokes lines for the Euler gamma function, in connection with the asymptotic expansion, are the positive and negative imaginary axes. On crossing these lines from the right to the left half-plane, infinitely many subdominant exponentials appear. The remainder of the asymptotic expansion is studied to describe this phenomenon. It is shown how an error function (as explained in a recent paper by Berry) can be used to clarify the transition from the right half-plane to the left half-plane. Numerical examples are included to illustrate the procedure.
[N.M.Temme (Amsterdam)]

MSC 2000:: *33B15 Gamma-functions, etc.
30E15 Asymptotic representations in the complex domain
41A60 Asymptotic problems in approximation

Keywords: Stokes lines; gamma function

Cited in: Zbl 0788.30028 Zbl 0772.30034

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