{"paper":{"title":"Close-to-convexity of some special functions and their derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"\\'Arp\\'ad Baricz, R\\'obert Sz\\'asz","submitted_at":"2014-02-04T11:09:05Z","abstract_excerpt":"In this paper our aim is to deduce some sufficient (and necessary) conditions for the close-to-convexity of some special functions and their derivatives, like Bessel functions, Struve functions, and a particular case of Lommel functions of the first kind, which can be expressed in terms of the hypergeometric function ${}_1F_2$. The key tool in our proofs is a result of Shah and Trimble about transcendental entire functions with univalent derivatives. Moreover, a known result of P\\'olya on entire functions, the infinite product representations and some results on zeros of Bessel, Struve and Lom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0692","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"}