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Zbl 0821.65006
Temme, N.M.
Computational aspects of incomplete gamma functions with large complex parameters. (English)
[A] Zahar, R. V. M. (ed.), Approximation and computation: a Festschrift in honor of Walter Gautschi. Proceedings of the Purdue conference, West Lafayette, IN, USA, December 2-5, 1993. Boston, US: Birkhäuser. ISNM, Int. Ser. Numer. Math. 119, 551-562 (1994). ISBN 0-8176-3753-2/hbk

To compute the incomplete gamma functions: $$\gamma (\alpha,z) = \int\sp z\sb 0 t\sp{\alpha - 1} e\sp{-t} dt, \quad \Gamma (\alpha,z) = \int\sp \infty\sb z t\sp{\alpha-1} e\sp{-t}dt,$$ several series expansions are introduced in this paper. Special considerations are given for asymptotic representations for large complex values of the parameter $\alpha$ and $z$.
[Y.Kobayashi (Tottori)]

MSC 2000:: *65D20 Computation of special functions
33B15 Gamma-functions, etc.
41A60 Asymptotic problems in approximation

Keywords: large complex parameters; asymptotic expansions; incomplete gamma functions; series expansions

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