Deaño, Alfredo,
Temme, Nico M.
(2009)
*
On modified asymptotic series involving confluent hypergeometric functions.
*
Electronic Transactions on Numerical Analysis,
35
.
pp. 88-103.
ISSN 1068-9613.
(The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
(KAR id:70236)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |

Official URL http://etna.mcs.kent.edu/volumes/2001-2010/vol35/a... |

## Abstract

A modification of the Poincaré-type asymptotic expansion for functions defined by Laplace transforms is analyzed. This modification is based on an alternative power series expansion of the integrand, and the convergence properties are seen to be superior to those of the original asymptotic series. The resulting modified asymptotic expansion involves a series of confluent hypergeometric functions U(a,c,z), which can be computed by means of continued fractions in a backward recursion scheme. Numerical examples are included, such as the incomplete gamma function ?(a,z) and the modified Bessel function K?(z) for large values of z. It is observed that the same procedure can be applied to uniform asymptotic expansions when extra parameters become large as well.

Item Type: | Article |
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Uncontrolled keywords: | confluent hypergeometric functions, asymptotic expansions, saddle point method, convergence and divergence of series and sequences |

Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA351 Special functions |

Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Alfredo Deano Cabrera |

Date Deposited: | 21 Nov 2018 11:01 UTC |

Last Modified: | 16 Nov 2021 10:25 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/70236 (The current URI for this page, for reference purposes) |

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

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