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On the stability of recurrence relations for 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.authorSegura, Javier
dc.date.accessioned2010-01-27T16:19:03Z
dc.date.available2010-01-27T16:19:03Z
dc.date.issued2005
dc.description4 pages, no figures.-- MSC2000 codes: 33C15, 33F05, 40A15.-- Running title: "Recurrences and continued fractions for Kummer functions".
dc.descriptionContributed to: ICNAAM 2005: Official conference of the European Society of Computational Methods in Sciences and Engineering (Rhodes, Greece, Sep 16-20, 2005).
dc.descriptionZbl#: Zbl 1086.33007
dc.description.abstractWe consider the three term recurrence relations y_n+1 + a_n y_n + b_n y_n-1 = 0 satisfied simultaneously by confluent hypergeometric functions M(a+kn; c+mn; x) and U(a+kn; c+mn; x) (up to normalizations not depending on x). The parameters a, c, x are fixed and k,m = 0,±1. The existence of minimal solutions when n -> ∞ is a crucial piece of information when we intend to use a recurrence relation for computation. However, in some cases the behavior of the solutions for moderate values of n can be opposite to the asymptotic behaviour. We provide numerical examples of this phenomenon, already noted by W. Gautschi in the case (k,m) = (1,1), both for the recurrence relations and for the associated continued fractions.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationSimos, Theodore S. (ed.) et al., ICNAAM 2005: International conference on numerical analysis and applied mathematics 2005, p. 672-675
dc.identifier.isbn3-527-40652-2
dc.identifier.urihttps://hdl.handle.net/10016/6657
dc.language.isoeng
dc.publisherWiley VCH
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherConfluent hypergeometric functions
dc.subject.otherContinued fractions
dc.subject.otherThree-term recurrence relations
dc.titleOn the stability of recurrence relations for hypergeometric functions
dc.typeconference paper*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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