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On modified asymptotic series involving confluent hypergeometric functions

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)

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. (Contact us about this Publication)
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
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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 21 Nov 2018 11:01 UTC
Last Modified: 30 May 2019 08:21 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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