{"paper":{"title":"A generalization of an identity due to Kimura and Ruehr","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean-Paul Allouche","submitted_at":"2017-06-27T16:28:22Z","abstract_excerpt":"An identity stated by Kimura and proved by Ruehr, Kimura and others stipulates that for any function $f$ continuous on $[-\\frac{1}{2}, \\frac{3}{2}]$ one has $$ \\int_{-1/2}^{3/2} f(3x^2 - 2x^3) dx = 2 \\int_0^1 f(3x^2 - 2x^3) dx. $$ We prove that this equality is not an isolated example by providing a family of polynomials, related to the Tchebychev polynomials and of which $(3x^2 - 2x^3)$ is a particular case, giving rise to similar identities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08929","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"}