{"paper":{"title":"Asymptotics for a Variant of the Mittag-Leffler Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CV","authors_text":"Stefan Gerhold","submitted_at":"2011-03-11T14:53:11Z","abstract_excerpt":"We generalize the Mittag-Leffler function by attaching an exponent to its Taylor coefficients. The main result is an asymptotic formula valid in sectors of the complex plane, which extends work by Le Roy [Bull. des sciences math. 24, 1900] and Evgrafov [Asimptoticheskie otsenki i tselye funktsii, 1979]. It is established by Plana's summation formula in conjunction with the saddle point method. As an application, we (re-)prove a non-holonomicity result about powers of the factorial sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2285","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"}