{"paper":{"title":"Asymptotical Bounds for Complete Elliptic Integrals of the Second Kind","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Miao-Kun Wang, Yu-Ming Chu","submitted_at":"2012-09-01T07:59:10Z","abstract_excerpt":"In this paper, we establish several asymptotical bounds for the complete elliptic integrals of the second kind $\\mathcal{E}(r)$, and improve the well-known conjecture $\\mathcal{E}(r)>\\pi[(1+(1-r^2)^{3/4})/2]^{2/3}/2$ for all $r\\in(0,1)$ proposed by M. Vuorinen."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0066","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"}