{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WVAS6ZYW4HATTM2CQ3NKEBUTAE","short_pith_number":"pith:WVAS6ZYW","schema_version":"1.0","canonical_sha256":"b5412f6716e1c139b34286daa206930111f46f017a4b9b85fb8e6529edd23f5b","source":{"kind":"arxiv","id":"1712.06474","version":1},"attestation_state":"computed","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 $\\{q_n (x)\\}_{n\\geq0"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.06474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-18T15:37:53Z","cross_cats_sorted":[],"title_canon_sha256":"7a2e013684a4015eab171f45e511ea5115b56fbc466f3c6cfd7eced79556588e","abstract_canon_sha256":"46e0367ef5d07d2c0204fe373d9e256b9ac61b00a0d7ae7a8136dd35e7d47d58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:47.774306Z","signature_b64":"Vss8ieJ1zjy5nnR/i+7umhutxjo8o5J2WB/KY+2Mck/puMmdYzlFK4R/wCtEXHXST13xp98PTYbBNzBXSHQgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5412f6716e1c139b34286daa206930111f46f017a4b9b85fb8e6529edd23f5b","last_reissued_at":"2026-05-18T00:27:47.773690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:47.773690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.06474","created_at":"2026-05-18T00:27:47.773789+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.06474v1","created_at":"2026-05-18T00:27:47.773789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06474","created_at":"2026-05-18T00:27:47.773789+00:00"},{"alias_kind":"pith_short_12","alias_value":"WVAS6ZYW4HAT","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WVAS6ZYW4HATTM2C","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WVAS6ZYW","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE","json":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE.json","graph_json":"https://pith.science/api/pith-number/WVAS6ZYW4HATTM2CQ3NKEBUTAE/graph.json","events_json":"https://pith.science/api/pith-number/WVAS6ZYW4HATTM2CQ3NKEBUTAE/events.json","paper":"https://pith.science/paper/WVAS6ZYW"},"agent_actions":{"view_html":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE","download_json":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE.json","view_paper":"https://pith.science/paper/WVAS6ZYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.06474&json=true","fetch_graph":"https://pith.science/api/pith-number/WVAS6ZYW4HATTM2CQ3NKEBUTAE/graph.json","fetch_events":"https://pith.science/api/pith-number/WVAS6ZYW4HATTM2CQ3NKEBUTAE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE/action/storage_attestation","attest_author":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE/action/author_attestation","sign_citation":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE/action/citation_signature","submit_replication":"https://pith.science/pith/WVAS6ZYW4HATTM2CQ3NKEBUTAE/action/replication_record"}},"created_at":"2026-05-18T00:27:47.773789+00:00","updated_at":"2026-05-18T00:27:47.773789+00:00"}