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12 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.A. Gil acknowledges financial support from Ministerio de Educación y Ciencia (programa Ramón y Cajal). J. Segura acknowledges financial support from project BFM2003-06335-C03-02. The authors acknowledge financial support from Ministerio de Educación y Ciencia (ProjectMTM2004–01367).Publicad

Computation of the Real Zeros of the Kummer Function M(a;c;x)