{"paper":{"title":"On generalized Lambert function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Alexander Kreinin, Andrey Marchenko, Vladimir Vinogradov","submitted_at":"2025-04-08T18:00:27Z","abstract_excerpt":"We consider a particular generalized Lambert function, $y(x)$, defined by the implicit equation $y^\\beta = 1 - e^{-xy}$, with $x>0$ and $ \\beta > 1$. Solutions to this equation can be found in terms of a certain continued exponential. Asymptotic and structural properties of a non-trivial solution, $y_\\beta(x)$, and its connection to the extinction probability of related branching processes are discussed. We demonstrate that this function constitutes a cumulative distribution function of a previously unknown non-negative absolutely continuous random variable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07142","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.07142/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}