{"paper":{"title":"Chebyshev Series Expansion of Inverse Polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Richard J. Mathar","submitted_at":"2004-03-22T02:40:14Z","abstract_excerpt":"An inverse polynomial has a Chebyshev series expansion\n 1/\\sum(j=0..k)b_j*T_j(x)=\\sum'(n=0..oo) a_n*T_n(x) if the polynomial has no roots in [-1,1]. If the inverse polynomial is decomposed into partial fractions, the a_n are linear combinations of simple functions of the polynomial roots. If the first k of the coefficients a_n are known, the others become linear combinations of these with expansion coefficients derived recursively from the b_j's. On a closely related theme, finding a polynomial with minimum relative error towards a given f(x) is approximately equivalent to finding the b_j in f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0403344","kind":"arxiv","version":4},"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"}