{"paper":{"title":"Infinite products involving binary digit sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Samin Riasat","submitted_at":"2017-09-13T01:37:01Z","abstract_excerpt":"Let $(u_n)_{n\\ge 0}$ denote the Thue-Morse sequence with values $\\pm 1$. The Woods-Robbins identity below and several of its generalisations are well-known in the literature \\begin{equation*}\\label{WR}\\prod_{n=0}^\\infty\\left(\\frac{2n+1}{2n+2}\\right)^{u_n}=\\frac{1}{\\sqrt 2}.\\end{equation*} No other such product involving a rational function in $n$ and the sequence $u_n$ seems to be known in closed form. To understand these products in detail we study the function \\begin{equation*}f(b,c)=\\prod_{n=1}^\\infty\\left(\\frac{n+b}{n+c}\\right)^{u_n}.\\end{equation*} We prove some analytical properties of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04104","kind":"arxiv","version":2},"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"}