{"paper":{"title":"Log-convexity and log-concavity of hypergeometric-like functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D.Karp, S.M. Sitnik","submitted_at":"2009-02-18T09:12:08Z","abstract_excerpt":"We find sufficient conditions for log-convexity and log-concavity for the functions of the forms $a\\mapsto\\sum{f_k}(a)_kx^k$, $a\\mapsto\\sum{f_k}\\Gamma(a+k)x^k$ and $a\\mapsto\\sum{f_k}x^k/(a)_k$. The most useful examples of such functions are generalized hypergeometric functions. In particular, we generalize the Tur\\'{a}n inequality for the confluent hypergeometric function recently proved by Barnard, Gordy and Richards and log-convexity results for the same function recently proved by Baricz. Besides, we establish a reverse inequality which complements naturally the inequality of Barnard, Gordy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3073","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"}