{"paper":{"title":"Recurrence Coefficients of the Orthogonal Polynomials for Oscillatory Jacobi-type Weight Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Shulin Lyu, Xun Zhou","submitted_at":"2026-07-22T06:21:21Z","abstract_excerpt":"We study two classes of oscillatory Jacobi-type weight functions $x^c(1-x^2)^{\\lambda-1/2}\\exp(i\\zeta x)$, $x\\in[-1,1], \\lambda>-1/2, c\\in\\{0,1\\}$. Other restrictions are imposed on $\\lambda$ and $\\zeta$ to guarantee the existence of the associated orthogonal polynomials. By using the ladder operators established in the recent literature for monic orthogonal polynomials associated with Jacobi-type weight functions and three compatibility conditions, we derive two coupled difference equations satisfied by the three-term recurrence coefficients. Compared with the existing results, these equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19797","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.19797/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}