Deaño Cabrera, AlfredoSegura, Javier2010-01-272010-01-272005Simos, Theodore S. (ed.) et al., ICNAAM 2005: International conference on numerical analysis and applied mathematics 2005, p. 672-6753-527-40652-2https://hdl.handle.net/10016/66574 pages, no figures.-- MSC2000 codes: 33C15, 33F05, 40A15.-- Running title: "Recurrences and continued fractions for Kummer functions".Contributed to: ICNAAM 2005: Official conference of the European Society of Computational Methods in Sciences and Engineering (Rhodes, Greece, Sep 16-20, 2005).Zbl#: Zbl 1086.33007We consider the three term recurrence relations y_n+1 + a_n y_n + b_n y_n-1 = 0 satisfied simultaneously by confluent hypergeometric functions M(a+kn; c+mn; x) and U(a+kn; c+mn; x) (up to normalizations not depending on x). The parameters a, c, x are fixed and k,m = 0,±1. The existence of minimal solutions when n -> ∞ is a crucial piece of information when we intend to use a recurrence relation for computation. However, in some cases the behavior of the solutions for moderate values of n can be opposite to the asymptotic behaviour. We provide numerical examples of this phenomenon, already noted by W. Gautschi in the case (k,m) = (1,1), both for the recurrence relations and for the associated continued fractions.application/pdfengConfluent hypergeometric functionsContinued fractionsThree-term recurrence relationsconference paperMatemáticasopen access