{"paper":{"title":"Starlikeness of the generalized Bessel function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Rosihan M. Ali, Saiful R. Mondal, See Keong Lee","submitted_at":"2017-07-03T02:19:51Z","abstract_excerpt":"For a fixed $a \\in \\{1, 2, 3, \\ldots\\},$ the radius of starlikeness of positive order is obtained for each of the normalized analytic functions \\begin{align*} \\mathtt{f}_{a, \\nu}(z)&:= \\bigg(2^{a \\nu-a+1} a^{-\\frac{a(a\\nu-a+1)}{2}} \\Gamma(a \\nu+1) {}_a\\mathtt{B}_{2a-1, a \\nu-a+1, 1}(a^{a/2} z)\\bigg)^{\\tfrac{1}{a \\nu-a+1}},\\\\ \\mathtt{g}_{a, \\nu}(z)&:= 2^{a \\nu-a+1} a^{-\\frac{a}{2}(a\\nu-a+1)} \\Gamma(a \\nu+1) z^{a-a\\nu} {}_a\\mathtt{B}_{2a-1, a \\nu-a+1, 1}(a^{a/2} z),\\\\ \\mathtt{h}_{a, \\nu}(z)&:= 2^{a \\nu-a+1} a^{-\\frac{a}{2}(a\\nu-a+1)} \\Gamma(a \\nu+1) z^{\\frac{1}{2}(1+a-a\\nu)} {}_a\\mathtt{B}_{2a-1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00379","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"}