{"paper":{"title":"Explicit representations of biorthogonal polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arieh Iserles, Syvert Paul N{\\o}rsett","submitted_at":"1994-04-22T00:00:00Z","abstract_excerpt":"Given a parametrised weight function $\\omega(x,\\mu)$ such that the quotients of its consecutive moments are M\\\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \\cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject to additional assumptions, every such $\\omega$ obeys (in $x$) a linear differential equation whose solution is a generalized hypergeometric function. Secondly, using a generalization of standard divided differences, we present a new explicit representation of the underlying orth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9404224","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"}