{"paper":{"title":"A note on an integral of Dixit, Roy and Zaharescu","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris","submitted_at":"2018-04-20T10:05:28Z","abstract_excerpt":"In a recent paper, Dixit {\\it et al.\\/} [Acta Arith. {\\bf 177} (2017) 1--37] posed two open questions whether the integral \\[{\\hat J}_{k}(\\alpha)=\\int_0^\\infty\\frac{xe^{-\\alpha x^2}}{e^{2\\pi x}-1}\\,{}_1F_1(-k,3/2;2\\alpha x^2)\\,dx\\] for $\\alpha>0$ could be evaluated in closed form when $k$ is a positive even and odd integer. We establish that ${\\hat J}_{k}(\\alpha)$ can be expressed in terms of a Gauss hypergeometric function and a ratio of two gamma functions, together with a remainder expressed as an integral. An upper bound on the remainder term is obtained, which is shown to be exponentially"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07527","kind":"arxiv","version":2},"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"}