Deaño, Alfredo and Gil, Amparo and Segura, Javier
(2006)
*
Computation of real zeros of the Kummer function M(a;c;x).
*
In:
Mathematical Software - ICMS 2006 Second International Congress on Mathematical Software.
Lecture Notes in Computer Science
.
Springer, Berlin, Germany, pp. 296-307.
ISBN 978-3-540-38084-9.
E-ISBN 978-3-540-38086-3.
(doi:10.1007/11832225_30)
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Official URL http://dx.doi.org/10.1007/11832225_30 |

## 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.

Item Type: | Book section |
---|---|

DOI/Identification number: | 10.1007/11832225_30 |

Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis Q Science > QA Mathematics (inc Computing science) > QA351 Special functions |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |

Depositing User: | Alfredo Deano-Cabrera |

Date Deposited: | 21 Nov 2018 10:42 UTC |

Last Modified: | 29 May 2019 13:41 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/70227 (The current URI for this page, for reference purposes) |

Deaño, Alfredo: | https://orcid.org/0000-0003-1704-247X |

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