{"paper":{"title":"Ramanujan and Extensions and Contractions of Continued Fractions","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin, Nancy J. Wyshinski","submitted_at":"2004-02-27T18:52:01Z","abstract_excerpt":"If a continued fraction $K_{n=1}^{\\infty} a_{n}/b_{n}$ is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\\infty}a_{n}/b_{n}$ to find the limit. By an extension of $K_{n=1}^{\\infty} a_{n}/b_{n}$ we mean a continued fraction $K_{n=1}^{\\infty} c_{n}/d_{n}$ whose odd or even part is $K_{n=1}^{\\infty} a_{n}/b_{n}$. One can then possibly find the limit in one of three ways:\n  (i) Prove the extension converges and find its limit;\n  (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402463","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"}