{"paper":{"title":"Symmetry and Specializability in the continued fraction expansions of some infinite products","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin","submitted_at":"2004-02-27T18:23:25Z","abstract_excerpt":"Let $f(x) \\in \\mathbb{Z}[x]$. Set $f_{0}(x) = x$ and, for $n \\geq 1$, define $f_{n}(x)$ $=$ $f(f_{n-1}(x))$. We describe several infinite families of polynomials for which the infinite product \\prod_{n=0}^{\\infty} (1 + \\frac{1}{f_{n}(x)}) has a \\emph{specializable} continued fraction expansion of the form S_{\\infty} = [1;a_{1}(x), a_{2}(x), a_{3}(x), ... ], where $a_{i}(x) \\in \\mathbb{Z}[x]$, for $i \\geq 1$. When the infinite product and the continued fraction are \\emph{specialized} by letting $x$ take integral values, we get infinite classes of real numbers whose regular continued fraction ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402459","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"}