{"paper":{"title":"Zeros of polynomials orthogonal with respect to a signed weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"M. Benabdallah, M. J. Atia, R. S. Costas-Santos","submitted_at":"2015-07-06T20:57:23Z","abstract_excerpt":"In this paper we consider the polynomial sequence $(P_{n}^{\\alpha,q}(x))$ that is orthogonal on $[-1,1]$ with respect to the weight function $x^{2q+1}(1-x^{2})^{\\alpha}(1-x), \\alpha>-1, q\\in \\mathbb N$; we obtain the coefficients of the tree-term recurrence relation (TTRR) by using a different method from the one derived in \\cite{kn:atia1}; we prove that the interlacing property does not hold properly for $(P_n^{\\alpha,q}(x))$; and we also prove that, if $x_{n,n}^{\\alpha+i,q+j}$ is the largest zero of $P_{n}^{\\alpha+i,q+j}(x)$, $\\displaystyle x_{2n-2j,2n-2j}^{\\alpha+j,q+j}< x_{2n-2i,2n-2i}^{\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01622","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"}