{"paper":{"title":"Asymptotics of a sum of modified Bessel functions with non-linear argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris","submitted_at":"2019-04-30T16:31:50Z","abstract_excerpt":"We examine the sum of modified Bessel functions with argument depending non-linearly on the summation index given by \\[S_{\\nu,p}(a)=\\sum_{n\\geq 1} (an^p/2)^{-\\nu} K_\\nu(an^p)\\qquad (a>0,\\ 0\\leq\\nu<1)\\] as the parameter $a\\to 0+$, where $p$ denotes an integer satisfying $p\\geq 2$. This extends previous work for the cases $p=1$ (linear) and $p=2$ (quadratic). The expansion as $a\\to0+$ consists of an infinite number of asymptotic sums involving the Riemann zeta function, which when optimally truncated lead to remainder terms that are exponentially small in the parameter $a$. The number of these e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00009","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"}