{"paper":{"title":"Classical and Sobolev Orthogonality of the Nonclassical Jacobi Polynomials with Parameters {\\alpha}={\\beta}=-1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CA","authors_text":"Andrea Bruder, Lance Littlejohn","submitted_at":"2012-05-23T02:37:41Z","abstract_excerpt":"In this paper, we consider the second-order differential expression\n  \\ell [y](x)=(1-x^2)(-(y'(x))'+k(1-x^2)^(-1)y(x))(x\\in(-1,1)).\n  This is the Jacobi differential expression with non-classical parameters {\\alpha} = {\\beta}= -1 in contrast to the classical case when {\\alpha}, {\\beta} > -1. For fixed k \\geq 0 and appropriate values of the spectral parameter {\\lambda}, the equation \\ell[y]={\\lambda}y has, as in the classical case, a sequence of (Jacobi) polynomial solutions {P_{n}^{(-1,-1)}}_{n=0}^{\\infty}. These Jacobi polynomial solutions of degree \\geq 2 form a complete orthogonal set in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5085","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"}