{"paper":{"title":"The general Brannan coefficient conjecture II: Meijer-function approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"T. M. Dunster","submitted_at":"2026-06-10T03:33:22Z","abstract_excerpt":"The coefficients $A_n(\\alpha,\\beta,\\omega)$ in the Maclaurin expansion $(1+\\omega z)^{\\alpha}(1-z)^{-\\beta}=\\sum_{n=0}^{\\infty} A_n(\\alpha,\\beta,\\omega)z^n$ are considered for $|\\omega|=1$ and $\\alpha,\\beta\\in(0,1]$. D. A. Brannan conjectured in a 1973 paper that $|A_n(\\alpha,\\beta,\\omega)|\\le A_n(\\alpha,\\beta,1)$ for every positive odd integer $n$. The present author recently established the conjecture outside a small neighbourhood of $\\omega=-1$. The remaining range is treated here by combining compound Laplace integral representations with two types of local approximation: a Meijer $G$ func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11621","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/2606.11621/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"}