{"paper":{"title":"$H_q-$semiclassical orthogonal polynomials via polynomial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"F. Marcell\\'an, J. Petronilho, K. Castillo, M. N. De Jesus","submitted_at":"2017-12-18T15:37:53Z","abstract_excerpt":"In this work we study orthogonal polynomials via polynomial mappings in the framework of the $H_q-$semiclassical class. We consider two monic orthogonal polynomial sequences $\\{p_n (x)\\}_{n\\geq0}$ and $\\{q_n(x)\\}_{n\\geq0}$ such that $$ p_{kn}(x)=q_n(x^k)\\;,\\quad n=0,1,2,\\ldots\\;, $$ being $k$ a fixed integer number such that $k\\geq2$, and we prove that if one of the sequences $\\{p_n (x)\\}_{n\\geq0}$ or $\\{q_n(x)\\}_{n\\geq0}$ is $H_q-$semiclassical, then so is the other one. In particular, we show that if $\\{p_n(x)\\}_{n\\geq0}$ is $H_q-$semiclassical of class $s\\leq k-1$, then $\\{q_n (x)\\}_{n\\geq0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06474","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"}