{"paper":{"title":"On series identities of Gosper and integrals of Ramanujan theta function $\\psi(q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mohamed El Bachraoui","submitted_at":"2018-12-16T05:46:06Z","abstract_excerpt":"We prove some Lambert series which were stated by Gosper without proof or reference. As an application, we shall evaluate integrals involving Ramanujan theta function $\\psi(q)$. Furthermore, motivated by Ramanujan's identities for $q\\psi^4(q^2)$ and $\\fr{\\psi^3(q)}{\\psi(q^3)}$, we shall evaluate the squares of $q\\psi^4(q^2)$ and $\\fr{\\psi^3(q)}{\\psi(q^3)}$ in terms of Lambert series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06396","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"}