Deaño Cabrera, AlfredoGil, AmparoSegura, Javier2010-01-272010-01-272006Lecture Notes in Computer Science, 2006, vol. 4151: Mathematical Software - ICMS 2006, p. 296-307978-3-540-38084-90302-9743 (Print)1611-3349 (Online)https://hdl.handle.net/10016/665312 pages, 5 figures.-- MSC2000 codes: Primary: 33F05; Secondary: 33C05, 34C60, 65H05.Contributed to: Second International Congress on Mathematical Software (ICMS'06, Castro Urdiales, Spain, Sep 1-3, 2006).MR#: MR2387180 (2009d:33060)An algorithm for computing the real zeros of the Kummer function M(a;c;x) is presented. The computation of ratios of functions of the type M(a+1; c+1; x)/M(a; c; x), M(a+1; c; x)/M(a; c; x) plays a key role in the algorithm, which is based on global fixed-point iterations. We analyse the accuracy and efficiency of three continued fraction representations converging to these ratios as a function of the parameter values. The condition of the change of variables appearing in the fixed point method is also studied. Comparison with implicit Maple functions is provided, including the Laguerre polynomial case.text/htmlengSpringerresearch articleMatemáticas10.1007/11832225open access