{"paper":{"title":"Exact & Numerical Tests of Generalised Root Identities for non-integer \\mu","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Richard Stone","submitted_at":"2011-11-07T12:09:50Z","abstract_excerpt":"We consider the generalised root identities introduced in [1] for simple functions, and also for \\Gamma(z+1) and \\zeta(s). In this paper, unlike [1], we focus on the case of noninteger \\mu. For the simplest function f(z)=z, and hence for arbitrary polynomials, we show that they are satisfied for arbitrary real {\\mu} (and hence for arbitrary complex {\\mu} by analytic continuation). Using this, we then develop an asymptotic formula for the derivative side of the root identities for \\Gamma(z+1) at arbitrary real \\mu, from which we are able to demonstrate numerically that \\Gamma(z+1) also satisfie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1950","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"}