{"paper":{"title":"Analysis of series expansions for non-algebraic singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Anthony J Guttmann","submitted_at":"2014-05-21T08:19:43Z","abstract_excerpt":"Existing methods of series analysis are largely designed to analyse the structure of algebraic singularities. Functions with such singularities have their $n^{th}$ coefficient behaving asymptotically as $A \\cdot \\mu^n \\cdot n^g.$ Recently, a number of problems in statistical mechanics and combinatorics have been encountered in which the coefficients behave asymptotically as $B \\cdot \\mu^n \\cdot \\mu_1^{n^\\sigma} \\cdot n^g,$ where typically $\\sigma = \\frac{1}{2}$ or $\\frac{1}{3}.$ Identifying this behaviour, and then extracting estimates for the critical parameters $B, \\,\\, \\mu, \\,\\, \\mu_1, \\,\\,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5327","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"}