{"paper":{"title":"Orthogonal polynomials associated to a certain fourth order differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CA","authors_text":"Gen Mano, Jan M\\\"ollers, Joachim Hilgert, Toshiyuki Kobayashi","submitted_at":"2009-07-15T15:06:32Z","abstract_excerpt":"We introduce orthogonal polynomials $M_j^{\\mu,\\ell}(x)$ as eigenfunctions of a certain self-adjoint fourth order differential operator depending on two parameters $\\mu\\in\\mathbb{C}$ and $\\ell\\in\\mathbb{N}_0$.\n  These polynomials arise as $K$-finite vectors in the $L^2$-model of the minimal unitary representations of indefinite orthogonal groups, and reduce to the classical Laguerre polynomials $L_j^\\mu(x)$ for $\\ell=0$.\n  We establish various recurrence relations and integral representations for our polynomials, as well as a closed formula for the $L^2$-norm. Further we show that they are uniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2612","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"}