{"paper":{"title":"Connection formulas for general discrete Sobolev polynomials. Mehler-Heine asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Pe\\~na, M.L. Rezola","submitted_at":"2014-11-12T10:17:47Z","abstract_excerpt":"In this paper the discrete Sobolev inner product $$< p,q > =\\int p(x) q(x) \\,d\\mu + \\sum_{i=0}^r M_i \\, p^{(i)}(c) \\, q^{(i)}(c)$$ is considered, where $\\mu$ is a finite positive Borel measure supported on an infinite subset of the real line, $c\\in\\mathbb{R}$ and $\\, M_i \\ge 0, \\, i = 0, 1, ..., r.$\n  Connection formulas for the orthonormal polynomials associated with $< ., . >$ are obtained. As a consequence, for a wide class of measures $\\mu$, we give the Mehler-Heine asymptotics in the case of the point $c$ is a hard edge of the support of $\\mu$. In particular, the case of a symmetric measu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3120","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}