{"paper":{"title":"The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Aleksandar V. Pejcev, Miodrag M. Spalevic, Ramon Orive","submitted_at":"2018-09-26T17:26:03Z","abstract_excerpt":"In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of anyone of the four Chebyshev weights, considered by Gautschi and Li in \\cite{gauli}. As it is well known, in the case of analytic integrands, the error of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel, as it is often considered, on elliptic contours with foci at the points $\\mp 1$ and such that the sum of semi-axes is $\\rho>1$, of the mentioned quadrature formulas, and derive some error bounds for them. In addition, we obtain, for the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10130","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"}