{"paper":{"title":"Partial sums of the normalized Dini functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Halit Orhan, \\.Ibrahim Akta\\c{s}","submitted_at":"2016-06-19T20:39:46Z","abstract_excerpt":"Let $\\left( w_{\\alpha ,v}\\right) _{m}(z)=z+\\sum\\limits_{n=1}^{m}a_{n}z^{n+1} $ be the sequence of partial sums of normalized Dini functions $w_{\\alpha ,v}(z)=z+\\sum\\limits_{n=1}^{\\infty }a_{n}z^{n+1}$ where $a_{n}=\\frac{\\left( -1\\right) ^{n}\\left( 2n+\\alpha \\right) }{\\alpha 4^{n}n!\\left( v+1\\right) _{n}% }$. The aim of the present paper is to obtain lower bounds for $\\mathcal{R} \\left\\{ \\frac{w_{\\alpha ,v}(z)}{\\left( w_{\\alpha ,v}\\right) _{m}(z)}\\right\\} ,$ $\\mathcal{R}\\left\\{ \\frac{\\left( w_{\\alpha ,v}\\right) _{m}(z)}{w_{\\alpha ,v}(z)}\\right\\} ,$ $\\mathcal{R}\\left\\{ \\frac{w_{\\alpha ,v}^{^{\\pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05906","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"}