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Further results on the computation of incomplete gamma functions. (English) Zbl 0597.33002
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.] 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.

33B15Gamma, beta and polygamma functions
30B70Continued fractions (function-theoretic results)
40A15Convergence and divergence of continued fractions
40D15Convergence factors; summability factors
41A20Approximation by rational functions
41A25Rate of convergence, degree of approximation
65B99Acceleration of convergence (numerical analysis)
65D20Computation of special functions, construction of tables