{"paper":{"title":"Recurrence Coefficients of a New Generalization of the Meixner Polynomials","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Galina Filipuk, Walter Van Assche","submitted_at":"2011-04-19T15:20:47Z","abstract_excerpt":"We investigate new generalizations of the Meixner polynomials on the lattice $\\mathbb{N}$, on the shifted lattice $\\mathbb{N}+1-\\beta$ and on the bi-lattice $\\mathbb{N}\\cup (\\mathbb{N}+1-\\beta)$. We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlev\\'e equation P$_{\\textup V}$. Initial conditions for different lattices can be transformed to the classical solutions of P$_{\\textup V}$ with special values of the parameters. We also study one property of the B\\\"acklund transformation of P$_{\\textup V}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3773","kind":"arxiv","version":2},"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"}