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Article Dans Une Revue Applied Numerical Mathematics Année : 2010

Asymptotic behaviours and general recurrence relations

Résumé

In this paper, we present some new results which give greater efficiency to our method – expanded in preceding papers, for studying some asymptotic behaviours of polynomials generated by recurrence relations. More precisely, we give some new results which show that, for the asymptotic of the polynomials satisfying recurrence relations, some interesting well-known studies in the literature can be extended to recurrence relations of other kinds. For example, in contrast with what is known, we explicitly show that there exist many families of polynomials, say {Mk}{Mk} and {Nk}{Nk} with MkMk a perturbation of NkNk such that limk→∞Mk(z)/Nk(z)=1limk→∞Mk(z)/Nk(z)=1 uniformly in a subset – which may be very large – of the complex plane and with conditions on perturbations which, to our knowledge, are new. We illustrate that by some surprising examples. This work also allows us to extend our analysis to other classes of orthogonal polynomials.

Dates et versions

hal-01277973 , version 1 (23-02-2016)

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Elie Léopold. Asymptotic behaviours and general recurrence relations. Applied Numerical Mathematics, 2010, 60 (12), pp.1352-1363. ⟨10.1016/j.apnum.2010.08.001⟩. ⟨hal-01277973⟩
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