On polynomials orthogonal with respect to certain Sobolev inner products
Journal of Approximation Theory
Determination of all coherent pairs
Journal of Approximation Theory
Strong and Plancherel—Rotach asymptotics of non-diagonal Laguerre—Sobolev orthogonal polynomials
Journal of Approximation Theory
Asymptotics of Sobolev orthogonal polynomials for Hermite coherent pairs
Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
Smallest zeros of some types of orthogonal polynomials: asymptotics
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Smallest zeros of some types of orthogonal polynomials: asymptotics
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
| Hi-index | 7.29 |
We consider a Sobolev inner product such as (f,g)s = ∫ f(x)g(x)dµ0(x) + λ ∫ f'(x)g'(x)dµ1(x), λ 0, µ1) being a symmetrically coherent pair of measures with unbounded support. Denote by Qn the orthogonal polynomials with respect to (1) and they are so-called Hermite-Sobolev orthogonal polynomials. We give a Mehler-Heine-type formula for Qn when µ1 is the measure corresponding to Hermite weight on R, that is, dµ1 = e-x2 dx and as a consequence an asymptotic property of both the zeros and critical points of Qn is obtained, illustrated by numerical examples. Some remarks and numerical experiments are carried out for dµ0 = e-x2 dx. An upper bound for |Qn| on R is also provided in both cases.