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.
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Deaño, A., Gil, A., Segura, J. (2006). Computation of the Real Zeros of the Kummer Function M(a;c;x). In: Iglesias, A., Takayama, N. (eds) Mathematical Software - ICMS 2006. ICMS 2006. Lecture Notes in Computer Science, vol 4151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11832225_30
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DOI: https://doi.org/10.1007/11832225_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38084-9
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