{"paper":{"title":"Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Antonio J. Dur\\'an","submitted_at":"2012-07-18T10:40:16Z","abstract_excerpt":"Let $(p_n)_n$ be a sequence of orthogonal polynomials with respect to the measure $\\mu$. Let $T$ be a linear operator acting in the linear space of polynomials $\\PP$ and satisfying that $\\dgr(T(p))=\\dgr(p)-1$, for all polynomial $p$. We then construct a sequence of polynomials $(s_n)_n$, depending on $T$ but not on $\\mu$, such that the Wronskian type $n\\times n$ determinant $\\det \\left(T^{i-1}(p_{m+j-1}(x))\\right)_{i,j=1}^n$ is equal to the $m\\times m$ determinant $\\det \\left(q^{j-1}_{n+i-1}(x)\\right)_{i,j=1}^m$, up to multiplicative constants, where the polynomials $q_n^i$, $n,i\\ge 0$, are de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4331","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"}