{"paper":{"title":"Linear partial $q$-difference equations on $q$-linear lattices and their bivariate $q$-orthogonal polynomial solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"E. Godoy, I. Area, J. Rodal, N. Atakishiyev","submitted_at":"2013-05-16T14:18:15Z","abstract_excerpt":"Orthogonal polynomial solutions of an admissible potentially self-adjoint linear second-order partial $q$-difference equation of the hypergeometric type in two variables on $q$-linear lattices are analyzed. A $q$-Pearson's system for the orthogonality weight function, as well as for the difference derivatives of the solutions are presented, giving rise to a solution of the $q$-difference equation under study in terms of a Rodrigues-type formula. The monic orthogonal polynomial solutions are treated in detail, giving explicit formulae for the matrices in the corresponding recurrence relations t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3819","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"}