Convergent expansions of the confluent hypergeometric functions in terms of elementary functions
Authors:
Blanca Bujanda, José L. López and Pedro J. Pagola
Journal:
Math. Comp. 88 (2019), 1773-1789
MSC (2010):
Primary 33C15; Secondary 41A58
DOI:
https://doi.org/10.1090/mcom/3389
Published electronically:
November 5, 2018
MathSciNet review:
3925484
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Abstract | References | Similar Articles | Additional Information
Abstract: We consider the confluent hypergeometric function for
and
, and the confluent hypergeometric function
for
,
, and
. We derive two convergent expansions of
; one of them in terms of incomplete gamma functions
and another one in terms of rational functions of
and
. We also derive a convergent expansion of
in terms of incomplete gamma functions
and
. The expansions of
hold uniformly in either
or
; the expansion of
holds uniformly in
. The accuracy of the approximations is illustrated by means of some numerical experiments.
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Additional Information
Blanca Bujanda
Affiliation:
Departamento de Estadística, Informática y Mathemáticas and InaMat, Universidad Pública de Navarra, Pamplona, Spain
Email:
blanca.bujanda@unavarra.es
José L. López
Affiliation:
Departamento de Estadística, Informática y Mathemáticas and InaMat, Universidad Pública de Navarra, Pamplona, Spain
Email:
jl.lopez@unavarra.es
Pedro J. Pagola
Affiliation:
Departamento de Estadística, Informática y Mathemáticas, Universidad Pública de Navarra, Pamplona, Spain
Email:
pedro.pagola@unavarra.es
DOI:
https://doi.org/10.1090/mcom/3389
Keywords:
Confluent hypergeometric functions,
convergent expansions,
uniform expansions
Received by editor(s):
October 25, 2017
Received by editor(s) in revised form:
May 2, 2018
Published electronically:
November 5, 2018
Additional Notes:
This research was supported by the Spanish Ministry of Economía y Competitividad, projects MTM2014-53178-P and TEC2013-45585-C2-1-R.
Article copyright:
© Copyright 2018
American Mathematical Society