{"paper":{"title":"Inequalities and Asymptotics for some Moment Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Faruk Abi-Khuzam","submitted_at":"2017-04-26T14:47:59Z","abstract_excerpt":"For $\\alpha>\\beta-1>0$, we obtain two sided inequalities for the moment integral $I(\\alpha,\\beta)= \\int_{\\mathbb{R}} |x|^{-\\beta}|\\sin x|^{\\alpha}dx$. These are then used to give the exact asymptotic behavior of the integral as $\\alpha \\to \\infty$. The case $I(\\alpha,\\alpha)$ corresponds to the asymptotics of Ball's inequality, and $I(\\alpha,[\\alpha]-1)$ corresponds to a kind of novel \"oscillatory\" behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08144","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"}