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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0402459","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2004-02-27T18:23:25Z","cross_cats_sorted":[],"title_canon_sha256":"1054e524ba33685bec65dffc6e2588b1d52f2e70ab330fbb1d686786204ecc8f","abstract_canon_sha256":"53a2d9321071cfbdd8b7e77a873864ff2efbb61a296442df0753d420371fbf55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:01.059423Z","signature_b64":"LCsIvmVwmEnVoIA/bifHitm5P7ZSISpwfMLdkIT5t8ui1uxIosabVnHgRc9qvH1lWjxLYToK/O8/RmW4VcwRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3752bb709421178a53bd84421370fcde48b665f4255fa06823a617b82af48f9f","last_reissued_at":"2026-05-17T23:57:01.058759Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:01.058759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $i \\geq 1$. 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