{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:52:16Z","timestamp":1776797536270,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"296","license":[{"start":{"date-parts":[[2016,4,15]],"date-time":"2016-04-15T00:00:00Z","timestamp":1460678400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We consider the Gauss-Radau quadrature formulae for the Bernstein-Szeg\u00f6 weight functions consisting of any one of the four Chebyshev weights divided by the polynomial\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"rho left-parenthesis t right-parenthesis equals 1 minus StartFraction 4 gamma Over left-parenthesis 1 plus gamma right-parenthesis squared EndFraction t squared comma negative 1 greater-than t greater-than 1 comma negative 1 greater-than gamma less-than-or-equal-to 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u03c1\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mfrac>\n                              <mml:mrow>\n                                <mml:mn>4<\/mml:mn>\n                                <mml:mi>\n                                  \u03b3\n                                  \n                                <\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow>\n                                <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mo>+<\/mml:mo>\n                                <mml:mi>\n                                  \u03b3\n                                  \n                                <\/mml:mi>\n                                <mml:msup>\n                                  <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                  <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                    <mml:mn>2<\/mml:mn>\n                                  <\/mml:mrow>\n                                <\/mml:msup>\n                              <\/mml:mrow>\n                            <\/mml:mfrac>\n                            <mml:msup>\n                              <mml:mi>t<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mtext>\u00a0<\/mml:mtext>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mtext>\u00a0<\/mml:mtext>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mi>\n                              \u03b3\n                              \n                            <\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\rho (t)=1-\\frac {4\\gamma }{(1+\\gamma )^{2}}t^{2},\\ -1&gt;t&gt;1,\\ -1&gt;\\gamma \\leq 0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . On certain spaces of analytic functions the error term of these formulae is a continuous linear functional. We compute or estimate the norm of the error functional.\n                  <\/p>","DOI":"10.1090\/mcom\/2944","type":"journal-article","created":{"date-parts":[[2015,4,15]],"date-time":"2015-04-15T07:53:17Z","timestamp":1429084397000},"page":"2843-2865","source":"Crossref","is-referenced-by-count":1,"title":["The error norm of Gauss-Radau quadrature formulae for Bernstein-Szeg\u00f6 weight functions"],"prefix":"10.1090","volume":"84","author":[{"given":"Sotirios","family":"Notaris","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2015,4,15]]},"reference":[{"key":"1","series-title":"Computational Mathematics and Applications","isbn-type":"print","volume-title":"Numerical quadrature and cubature","author":"Engels, H.","year":"1980","ISBN":"https:\/\/id.crossref.org\/isbn\/012238850X"},{"key":"2","isbn-type":"print","first-page":"72","article-title":"A survey of Gauss-Christoffel quadrature formulae","author":"Gautschi, Walter","year":"1981","ISBN":"https:\/\/id.crossref.org\/isbn\/3764311622"},{"key":"3","isbn-type":"print","first-page":"133","article-title":"Remainder estimates for analytic functions","author":"Gautschi, Walter","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0792315839"},{"key":"#cr-split#-4.1","doi-asserted-by":"crossref","unstructured":"W. Gautschi, \"Algorithm 726: ORTHPOL - a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules\", ACM Trans. Math. Software, 20 (1994), no. 1, 21-62","DOI":"10.1145\/174603.174605"},{"key":"#cr-split#-4.2","doi-asserted-by":"crossref","unstructured":"\"Remark on algorithm 726: ORTHPOL - a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules\", ACM Trans. Math. Software, 24 (1998), no. 3, 355-356.","DOI":"10.1145\/292395.292467"},{"key":"5","series-title":"Numerical Mathematics and Scientific Computation","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198506720.001.0001","volume-title":"Orthogonal polynomials: computation and approximation","author":"Gautschi, Walter","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/0198506724"},{"issue":"2","key":"6","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0377-0427(89)90047-2","article-title":"Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szeg\u0151 type","volume":"25","author":"Gautschi, Walter","year":"1989","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"7","isbn-type":"print","volume-title":"Table of integrals, series, and products","author":"Gradshteyn, I. S.","year":"1980","ISBN":"https:\/\/id.crossref.org\/isbn\/0122947606"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/BF01386411","article-title":"The error norm of Gaussian quadrature formulae for weight functions of Bernstein-Szeg\u0151 type","volume":"57","author":"Notaris, Sotirios E.","year":"1990","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"1","key":"9","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s00211-005-0670-x","article-title":"The error norm of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szeg\u0151 type","volume":"103","author":"Notaris, Sotirios E.","year":"2006","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"1","key":"10","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s10543-010-0252-x","article-title":"The error norm of Gauss-Radau quadrature formulae for Chebyshev weight functions","volume":"50","author":"Notaris, Sotirios E.","year":"2010","journal-title":"BIT","ISSN":"https:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"},{"issue":"4","key":"11","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1007\/s11075-012-9582-x","article-title":"The error norm of quadrature formulae","volume":"60","author":"Notaris, Sotirios E.","year":"2012","journal-title":"Numer. Algorithms","ISSN":"https:\/\/id.crossref.org\/issn\/1017-1398","issn-type":"print"},{"key":"12","series-title":"American Mathematical Society Colloquium Publications, Vol. XXIII","volume-title":"Orthogonal polynomials","author":"Szeg\u0151, G\u00e1bor","year":"1975","edition":"4"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2015-84-296\/S0025-5718-2015-02944-5\/S0025-5718-2015-02944-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2015-84-296\/S0025-5718-2015-02944-5\/S0025-5718-2015-02944-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:33:17Z","timestamp":1776796397000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2015-84-296\/S0025-5718-2015-02944-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,15]]},"references-count":13,"journal-issue":{"issue":"296","published-print":{"date-parts":[[2015,11]]}},"alternative-id":["S0025-5718-2015-02944-5"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/2944","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2015,4,15]]}}}