{"paper":{"title":"Properties of the zeros of generalized basic hypergeometric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Francesco Calogero, Oksana Bihun","submitted_at":"2015-04-07T20:17:42Z","abstract_excerpt":"We define the generalized basic hypergeometric polynomial of degree $N \\geq 1$ in terms of the generalized basic hypergeometric function, which depends on (arbitrary, generic, possibly complex) parameters $q \\neq 1$, the $r \\geq 0$ parameters $\\alpha _{j}$ and the $s \\geq 0$ parameters $\\beta _{k}$. In this paper we obtain a set of $N$ nonlinear algebraic equations satisfied by the $N$ zeros $\\zeta _{n}\\equiv \\zeta _{n}\\left( \\underline{\\alpha },\\underline{\\beta };q;N\\right) $ of this polynomial. We moreover identify an $\\left( N\\times N\\right) $-matrix $\\underline{M}\\equiv \\underline{M}\\left("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01748","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"}