Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4626472 | Applied Mathematics and Computation | 2015 | 15 Pages |
Abstract
In this paper the discrete Sobolev inner product 〈p,q〉=∫p(x)q(x)dμ+∑i=0rMip(i)(c)q(i)(c)is considered, where μ is a finite positive Borel measure supported on an infinite subset of the real line, c∈Rc∈R and Mi ≥ 0, i = 0, 1, …, r.Connection formulas for the orthonormal polynomials associated with 〈., .〉 are obtained. As a consequence, for a wide class of measures μ, we give the Mehler–Heine asymptotics in the case of the point c is a hard edge of the support of μ. In particular, the case of a symmetric measure μ is analyzed. Finally, some examples are presented.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
A. Peña, M.L. Rezola,