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On modified asymptotic series involving confluent hypergeometric functions

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorDeaño Cabrera, Alfredo
dc.contributor.authorTemme, Nico M.
dc.date.accessioned2010-01-26T12:12:21Z
dc.date.available2010-01-26T12:12:21Z
dc.date.issued2009
dc.description16 pages, 5 figures.-- MSC2000 codes: 33C15, 33F99, 34E05, 30E15, 40A05.
dc.description.abstractA modification of standard Poincaré asymptotic expansions for functions defined by means of 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 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 Γ(a,z) and the modified Bessel function Kv(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.
dc.description.sponsorshipThe first author acknowledges financial support from the Program of postdoctoral research grants (Programa de becas postdoctorales) of the Spanish Ministry of Education and Science (Ministerio de Educación y Ciencia). The authors acknowledge financial support from the Spanish Ministry of Education and Science (Ministerio de Educación y Ciencia), under project MTM2006–09050.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationElectronic Transactions on Numerical Analysis, 2009, vol. 35, p. 88-103
dc.identifier.issn1068-9613
dc.identifier.urihttps://hdl.handle.net/10016/6637
dc.language.isoeng
dc.publisherKent State University
dc.relation.publisherversionhttp://www.emis.de/journals/ETNA/vol.35.2009/pp88-103.dir/pp88-103.pdf
dc.rights© Kent State University
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherConfluent hypergeometric functions
dc.subject.otherAsymptotic expansions
dc.subject.otherSaddle point method
dc.subject.otherConvergence and divergence of series and sequences
dc.titleOn modified asymptotic series involving confluent hypergeometric functions
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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