Computation of the real zeros of the kummer function M(a; c; x)

Authors:
Alfredo Deaño;Amparo Gil;Javier Segura
Affiliations:
Departamento de Matemáticas, Univ. Carlos III de Madrid, Leganés (Madrid), Spain;Departamento de Matemáticas, Estadística y Computación. Univ. de Cantabria., Santander, Spain;Departamento de Matemáticas, Estadística y Computación. Univ. de Cantabria., Santander, Spain
Venue:
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Year:
2006

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Abstract

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.