{"paper":{"title":"On difference equations of Kravchuk-Sobolev type polynomials of higher order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Anier Soria-Lorente, Roberto S. Costas-Santos","submitted_at":"2020-10-31T12:08:24Z","abstract_excerpt":"In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product \\[ \\left\\langle f,g\\right\\rangle _{\\lambda,\\mu}\\!=\\!\\sum_{x=0}^Nf(x)g(x)\\frac{\\Gamma(N+1) p^x(1-p)^{N-x} }{\\Gamma (N-x+1) \\Gamma(x+1) }+\\lambda\\Delta^j f(0)\\Delta^j g(0)+\\mu\\Delta^j f(N)\\Delta^j g(N), \\] where $0<p <1$, $\\lambda,\\mu\\in \\mathbb R_{+}$, $n\\leq N\\in \\mathbb Z_{+}$, $j\\in \\mathbb Z_{+}$ and $\\Delta$ denotes the forward difference operators. We derive an explicit representation for these polynomials. In addition, the ladder operators associated with these polynomial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.00255","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/2011.00255/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"}