{"paper":{"title":"On another extension of coherent pairs of measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. Mbouna, K. Castillo","submitted_at":"2019-06-18T17:57:54Z","abstract_excerpt":"Let $M$ and $N$ be fixed non-negative integer numbers and let $\\pi_N$ be a polynomial of degree $N$. Suppose that $(P_n)_{n\\geq0}$ and $(Q_n)_{n\\geq0}$ are two orthogonal polynomial sequences such that %their derivatives of orders $k$ and $m$ (respectively) satisfy the structure relation $$ \\pi_N(x)\\,P_{n+m}^{(m)}(x)= \\sum_{j=n-M}^{n+N}r_{n,j}Q_{j+k}^{(k)}(x)\\quad (n=0,1,\\ldots)\\,, $$ where $r_{n,j}$ are complex number independent of $x$. It is shown that under natural constraints, $(P_n)_{n\\geq0}$ and $(Q_n)_{n\\geq0}$ are semiclassical orthogonal polynomial sequences. Moreover, their correspo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07715","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"}