{"paper":{"title":"On some results for meromorphic univalent functions having quasiconformal extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Goutam Satpati","submitted_at":"2017-05-10T08:41:02Z","abstract_excerpt":"We consider the class $\\Sigma(p)$ of univalent meromorphic functions $f$ on $\\ID$ having simple pole at $z=p\\in[0,1)$ with residue 1. Let $\\Sigma_k(p)$ be the class of functions in $\\Sigma(p)$ which have $k$-quasiconformal extension to the extended complex plane $\\sphere$ %with $q=\\frac{1+k}{1-k}$ where $0\\leq k < 1$. We first give a representation formula for functions in this class and using this formula we derive an asymptotic estimate of the Laurent coefficients for the functions in the class $\\Sigma_k(p)$. Thereafter we give a sufficient condition for functions in $\\Sigma(p)$ to belong in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03660","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"}