{"paper":{"title":"Tur\\'an type inequalities for Kr\\\"atzel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"\\'Arp\\'ad Baricz, Dragana Jankov, Tibor K. Pog\\'any","submitted_at":"2011-01-13T10:05:39Z","abstract_excerpt":"Complete monotonicity, Laguerre and Tur\\'an type inequalities are established for the so-called Kr\\\"atzel function $Z_{\\rho}^{\\nu},$ defined by $$Z_{\\rho}^{\\nu}(u)=\\int_0^{\\infty}t^{\\nu-1}e^{-t^{\\rho}-\\frac{u}{t}}\\dt,$$ where $u>0$ and $\\rho,\\nu\\in\\mathbb{R}.$ Moreover, we prove the complete monotonicity of a determinant function of which entries involve the Kr\\\"atzel function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2523","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"}