{"paper":{"title":"$*$-exponential of slice-regular functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Amedeo Altavilla, Chiara de Fabritiis","submitted_at":"2018-06-27T12:55:02Z","abstract_excerpt":"According to [5] we define the $*$-exponential of a slice-regular function, which can be seen as a generalization of the complex exponential to quaternions. Explicit formulas for $\\exp_*(f)$ are provided, also in terms of suitable sine and cosine functions. We completely classify under which conditions the $*$-exponential of a function is either slice-preserving or $\\mathbb{C}_J$-preserving for some $J\\in\\mathbb{S}$ and show that $\\exp_*(f)$ is never-vanishing. Sharp necessary and sufficient conditions are given in order that $\\exp_*(f+g)=\\exp_*(f)*\\exp_*(g)$, finding an exceptional and unexpe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10446","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"}