{"paper":{"title":"Definite Sums as Solutions of Linear Recurrences With Polynomial Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Marko Petkov\\v{s}ek","submitted_at":"2018-04-09T13:17:15Z","abstract_excerpt":"We present an algorithm which, given a linear recurrence operator $L$ with polynomial coefficients, $m \\in \\mathbb{N}\\setminus\\{0\\}$, $a_1,a_2,\\ldots,a_m \\in \\mathbb{N}\\setminus\\{0\\}$ and $b_1,b_2,\\ldots,b_m \\in \\mathbb{K}$, returns a linear recurrence operator $L'$ with rational coefficients such that for every sequence $h$, \\[ L\\left(\\sum_{k=0}^\\infty \\prod_{i=1}^m \\binom{a_i n + b_i}{k} h_k\\right) = 0 \\] if and only if $L' h = 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02964","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"}