Laguerre–Sobolev orthogonal polynomials: asymptotics for coherent pairs of type II
✍ Scribed by Manuel Alfaro; Juan J. Moreno-Balcázar; M.Luisa Rezola
- Book ID
- 108332836
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 209 KB
- Volume
- 122
- Category
- Article
- ISSN
- 0021-9045
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📜 SIMILAR VOLUMES
Let {Sn}n denote a sequence of polynomials orthogonal with respect to the Sobolev inner product where ¿ 0 and {d 0; d 1} is a so-called coherent pair with at least one of the measures d 0 or d 1 a Jacobi measure. We investigate the asymptotic behaviour of Sn(x), for n → +∞ and x ÿxed, x ∈ C \ [ -1;
Strong asymptotics for the sequence of monic polynomials Q n (z), orthogonal with respect to the inner product with z outside of the support of the measure + 2 , is established under the additional assumption that + 1 and + 2 form a so-called coherent pair with compact support. Moreover, the asympt
Let {S,} denote the sequence of polynomials orthogonal with respect to the Sobolev inner product fo +°° f+°c :,. x . ,.x--%-X dx (f.g)s = f(x)o(x)x%-Xdx + 2 J ~ )9( )x . ## JO where ~ > -1, 2 > 0 and the leading coefficient of the S~ is equal to the leading coefficient of the Laguerre polynomial