{"paper":{"title":"On the asymptotics of Bessel functions in the Fresnel regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.NA","authors_text":"Bogdan Vioreanu, James Bremer, Jhu Heitman, Vladimir Rokhlin","submitted_at":"2014-09-14T20:26:49Z","abstract_excerpt":"We introduce a version of the asymptotic expansions for Bessel functions $J_\\nu(z)$, $Y_\\nu(z)$ that is valid whenever $|z| > \\nu$ (which is deep in the Fresnel regime), as opposed to the standard expansions that are applicable only in the Fraunhofer regime (i.e. when $|z| > \\nu^2$). As expected, in the Fraunhofer regime our asymptotics reduce to the classical ones. The approach is based on the observation that Bessel's equation admits a non-oscillatory phase function, and uses classical formulas to obtain an asymptotic expansion for this function; this in turn leads to both an analytical tool"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4100","kind":"arxiv","version":3},"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"}