{"paper":{"title":"Lemniscate Convexity and Other Properties of Generalized Bessel Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ajay Kumar, Vibha Madaan, V. Ravichandran","submitted_at":"2019-02-12T08:32:56Z","abstract_excerpt":"Sufficient conditions on associated parameters $p,b$ and $c$ are obtained so that the generalized and \\textquotedblleft{normalized}\\textquotedblright{} Bessel function $u_p(z)=u_{p,b,c}(z)$ satisfies $|(1+(zu''_p(z)/u'_p(z)))^2-1|<1$ or $|((zu_p(z))'/u_p(z))^2-1|<1$. We also determine the condition on these parameters so that $-(4(p+(b+1)/2)/c)u'_p(z)\\prec\\sqrt{1+z}$. Relations between the parameters $\\mu$ and $p$ are obtained such that the normalized Lommel function of first kind $h_{\\mu,p}(z)$ satisfies the subordination $1+(zh''_{\\mu,p}(z)/h'_{\\mu,p}(z))\\prec\\sqrt{1+z}$. Moreover, the prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04277","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"}