{"paper":{"title":"Properties of reciprocity formulas for the Rogers-Ramanujan continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rajeev Kohli","submitted_at":"2018-06-14T20:41:23Z","abstract_excerpt":"Ramanujan recorded four reciprocity formulas for the Roger-Ramanujan continued fraction. Two reciprocity formulas each are also associated with the Ramanujan--G\\\"ollnitz--Gordon continued fraction and a level-13 analog of the Roger-Ramanujan continued fraction. We show that all eight reciprocity formulas are related to a pair of quadratic equations. The solution to the first equation generalizes the golden ratio and is used to set the value of a coefficient in the second equation; and the solution to the second equation gives a pair of values for a continued fraction. We relate the coefficient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05739","kind":"arxiv","version":7},"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"}