Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509689 | Journal of Computational and Applied Mathematics | 2005 | 16 Pages |
Abstract
Let {Qn(x)}n be the sequence of monic polynomials orthogonal with respect to the Sobolev-type inner productãp(x),r(x)ãS=ãu0,p(x)r(x)ã+λãu1,(Îp)(x)(Îr)(x)ã,where λ⩾0, (Îf)(x)=f(x+1)-f(x) denotes the forward difference operator and (u0,u1) is a Î-coherent pair of positive-definite linear functionals being u1 the Meixner linear functional. In this paper, relative asymptotics for the {Qn(x)}n sequence with respect to Meixner polynomials on compact subsets of C⧹[0,+â) is obtained. This relative asymptotics is also given for the scaled polynomials. In both cases, we deduce the same asymptotics as we have for the self-Î-coherent pair, that is, when u0=u1 is the Meixner linear functional. Furthermore, we establish a limit relation between these orthogonal polynomials and the Laguerre-Sobolev orthogonal polynomials which is analogous to the one existing between Meixner and Laguerre polynomials in the Askey scheme.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
I. Area, E. Godoy, F. Marcellán, J.J. Moreno-Balcázar,