{"paper":{"title":"Approximating the coefficients of the Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.OA","math.PR"],"primary_cat":"math.CA","authors_text":"Andrew Yao","submitted_at":"2025-10-11T23:46:56Z","abstract_excerpt":"We determine equivalent conditions between the asymptotic coefficients of the Bessel generating functions of a sequence of probability measures and the asymptotic expected values of power sums when their inputs are sampled from these measures. We establish these conditions over the $|\\theta N| \\rightarrow\\infty$ regime for the type A and D root systems and over the $|\\theta_0 N|\\rightarrow \\infty, \\frac{\\theta_1}{\\theta_0 N}\\rightarrow c\\in\\mathbb{C}$ regime for the type BC root system. We also establish equivalent conditions over the $\\theta N \\rightarrow c\\in\\mathbb{C}$ regime for the type A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.10370","kind":"arxiv","version":6},"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/2510.10370/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"}