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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

Γ(a,z)= z e -t t a-1 dt,a,|argz|<π,

can be expressed by means of a Stieltjes fraction K(α n z -1 /1), where α 1 =1, α 2n =n-a and α 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(α n z -1 /1) considerably.


MSC:
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