{"paper":{"title":"Lifting Bailey Pairs to WP-Bailey Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew V. Sills, James Mc Laughlin, Peter Zimmer","submitted_at":"2019-01-04T01:23:13Z","abstract_excerpt":"A pair of sequences $(\\alpha_{n}(a,k,q),\\beta_{n}(a,k,q))$ such that $\\alpha_0(a,k,q)=1$ and \\[ \\beta_{n}(a,k,q) = \\sum_{j=0}^{n} \\frac{(k/a; q)_{n-j}(k; q)_{n+j}}{(q;q)_{n-j}(aq;q)_{n+j}}\\alpha_{j}(a,k,q) \\] is termed a \\emph{WP-Bailey Pair}. Upon setting $k=0$ in such a pair we obtain a \\emph{Bailey pair}. In the present paper we consider the problem of \"lifting\" a Bailey pair to a WP-Bailey pair, and use some of the new WP-Bailey pairs found in this way to derive some new identities between basic hypergeometric series and new single sum- and double sum identities of the Rogers-Ramanujan-Sla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04841","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"}