{"paper":{"title":"An Identity Motivated by an Amazing Identity of Ramanujan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin","submitted_at":"2019-01-04T23:57:52Z","abstract_excerpt":"Ramanujan stated an identity to the effect that if three sequences $\\{a_n\\}$, $\\{b_n\\}$ and $\\{c_n\\}$ are defined by $r_1(x)=:\\sum_{n=0}^{\\infty}a_nx^n$, $r_2(x)=:\\sum_{n=0}^{\\infty}b_nx^n$ and $r_3(x)=:\\sum_{n=0}^{\\infty}c_nx^n$ (here each $r_i(x)$ is a certain rational function in $x$), then \\[ a_n^3+b_n^3-c_n^3=(-1)^n, \\hspace{25pt} \\forall \\,n \\geq 0. \\] Motivated by this amazing identity, we state and prove a more general identity involving eleven sequences, the new identity being \"more general\" in the sense that equality holds not just for the power 3 (as in Ramanujan's identity), but fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04842","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"}