{"paper":{"title":"Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","nlin.SI","quant-ph"],"primary_cat":"math.CA","authors_text":"C.-L. Ho, K. Takemura, R. Sasaki","submitted_at":"2012-09-30T14:48:41Z","abstract_excerpt":"The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\\\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of the P\\\"oschl-Teller potential, we obtain several families of explicit and global solutions of certain second order Fuchsian differential equations with an apparent singularity of characteristic exponent -2 and -1. They form orthogonal polynomials over $x\\in(-1,1)$ with weight functions of the form $(1-x)^\\alpha(1+x)^\\beta/\\{(ax+b)^4q(x)^2\\}$, in which $q(x)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0207","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"}