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Zbl 0597.33002
Jacobsen, Lisa; Jones, William B.; Waadeland, Haakon
Further results on the computation of incomplete gamma functions. (English)
[A] Analytic theory of continued fractions II, Proc. Semin.-Workshop, Pitlochry and Aviemore/Scotl. 1985, Lect. Notes Math. 1199, 67-89 (1986).

[For the entire collection see Zbl 0583.00009.] \par The complementary incomplete gamma function $$ \Gamma (a,z)=\int\sp{\infty}\sb{z}e\sp{-t}t\sp{a-1} dt,\quad a\in {\bbfC},\quad \vert \arg z\vert <\pi,$$ can be expressed by means of a Stieltjes fraction $K(\alpha\sb nz\sp{-1}/1),$ where $\alpha\sb 1=1,$ $\alpha\sb{2n}=n-a$ and $\alpha\sb{2n+1}=n.$ We investigate convergence, truncation error bounds and speed of convergence for these and related continued fractions. Moreover, we suggest a modifying factor which is easy to compute and which accelerates the convergence of $K(\alpha\sb nz\sp{-1}/1)$ considerably.

MSC 2000:: *33B15 Gamma-functions, etc.
30B70 Continued fractions (function-theoretic results)
40A15 Convergence of continued fractions
40D15 Convergence factors and summability factors
41A20 Approximation by rational functions
41A25 Degree of approximation, etc.
65B99 Acceleration of convergence
65D20 Computation of special functions

Keywords: convergence acceleration; gamma function; Stieltjes fraction; truncation error bounds

Citations: Zbl 0583.00009

Cited in: Zbl 0662.30002

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