{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T21:53:31Z","timestamp":1758405211198},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2009,2,25]],"date-time":"2009-02-25T00:00:00Z","timestamp":1235520000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2009,11]]},"DOI":"10.1007\/s11075-009-9273-4","type":"journal-article","created":{"date-parts":[[2009,2,24]],"date-time":"2009-02-24T07:05:50Z","timestamp":1235459150000},"page":"273-293","source":"Crossref","is-referenced-by-count":4,"title":["An application of Szeg\u0151 polynomials to the computation of certain weighted integrals on the real line"],"prefix":"10.1007","volume":"52","author":[{"given":"R.","family":"Cruz-Barroso","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Gonz\u00e1lez-Vera","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Perdomo-P\u00edo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,2,25]]},"reference":[{"key":"9273_CR1","unstructured":"Alfaro, M.: Una expresi\u00f3n de los polinomios ortogonales sobre la circunferencia unidad. Actas de las Terceras Jornadas Matem\u00e1ticas Hispano-Lusitanas, pp. 1\u20138. Terceras Jornadas Matem\u00e1ticas Hispano-Lusitanas, Sevilla (1974)"},{"key":"9273_CR2","doi-asserted-by":"crossref","first-page":"L611","DOI":"10.1088\/0305-4470\/27\/17\/003","volume":"27","author":"N.M. Atkishiyev","year":"1994","unstructured":"Atkishiyev, N.M., Nagiyev, S.M.: On Rogers-Szeg\u0151 polynomials. J. Phys. A Math. Gen. 27, L611\u2013L615 (1994)","journal-title":"J. Phys. A Math. Gen."},{"key":"9273_CR3","first-page":"1","volume":"132","author":"A. Bultheel","year":"2001","unstructured":"Bultheel, A., Daruis, L., Gonz\u00e1lez-Vera, P.: A connection between quadrature formulas on the unit circle and the interval [\u2009\u2212\u20091,1]. Appl. Numer. Math. 132, 1\u201314 (2001)","journal-title":"Appl. Numer. Math."},{"key":"9273_CR4","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.cam.2004.09.037","volume":"179","author":"A. Bultheel","year":"2005","unstructured":"Bultheel, A., Daruis, L., Gonz\u00e1lez-Vera, P.: Positive interpolatory quadrature formulas and para-orthogonal polynomials. J. Comp. Appl. Math. 179, 97\u2013119 (2005)","journal-title":"J. Comp. Appl. Math."},{"key":"9273_CR5","unstructured":"Bultheel, A., Gonz\u00e1lez-Vera, P., Hendriksen, E., Nj\u00e5stad, O.: Orthogonality and quadrature on the unit circle. In: Brezinski, C., Gori, L., Ronveaux, A. (eds.) Orthogonal Polynomials and Their Applications, IMACS Ann. Comput. Appl. Math., vol. 9, pp. 205\u2013210. Baltzer, Basel (1991)"},{"key":"9273_CR6","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1524\/anly.1998.18.2.185","volume":"18","author":"A. Bultheel","year":"1998","unstructured":"Bultheel, A., Gonz\u00e1lez-Vera, P., Hendriksen, E., Nj\u00e5stad, O.: Orthogonal rational functions and interpolatory product rules on the unit circle.\u2014II: quadrature and convergence. Analysis 18, 185\u2013200 (1998)","journal-title":"Analysis"},{"key":"9273_CR7","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1524\/anly.2000.20.2.99","volume":"20","author":"A. Bultheel","year":"2000","unstructured":"Bultheel, A., Gonz\u00e1lez-Vera, P., Hendriksen, E., Nj\u00e5stad, O.: Orthogonal rational functions and interpolatory product rules on the unit circle.\u2014III: convergence of general sequences. Analysis 20, 99\u2013120 (2000)","journal-title":"Analysis"},{"issue":"3","key":"9273_CR8","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.apnum.2006.11.009","volume":"58","author":"M.J. Cantero","year":"2008","unstructured":"Cantero, M.J., Cruz-Barroso, R., Gonz\u00e1lez-Vera, P.: A matrix approach to the computation of quadrature formulas on the unit circle. Appl. Numer. Math. 58(3), 296\u2013318 (2008)","journal-title":"Appl. Numer. Math."},{"key":"9273_CR9","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.cam.2006.01.008","volume":"200","author":"R. Cruz-Barroso","year":"2007","unstructured":"Cruz-Barroso, R., Daruis, L., Gonz\u00e1lez-Vera, P., Nj\u00e5stad, O.: Sequences of orthogonal Laurent polynomials, bi-orthogonality and quadrature formulas on the unit circle. J. Comput. Appl. Math. 200, 424\u2013440 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"9273_CR10","doi-asserted-by":"crossref","unstructured":"Cruz-Barroso, R., Delvaux, S.: Orthogonal Laurent polynomials on the unit circle and snake-shaped matrix factorizations. J. Approx. Theory (2009). doi: 10.1016\/j.jat.2008.08.004","DOI":"10.1016\/j.jat.2008.08.004"},{"key":"9273_CR11","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/j.camwa.2008.10.068","volume":"57","author":"R. Cruz-Barroso","year":"2009","unstructured":"Cruz-Barroso, R., Gonz\u00e1lez-Vera, P., Perdomo-P\u00edo, F.: Quadrature formulas associated with Rogers-Szeg\u0151 polynomials. Comp. Math. Appl. 57, 308\u2013323 (2009)","journal-title":"Comp. Math. Appl."},{"key":"9273_CR12","volume-title":"Methods of Numerical Integration","author":"P.J. Davis","year":"1984","unstructured":"Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration. Academic, New York (1984)"},{"key":"9273_CR13","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/s00211-007-0102-1","volume":"107","author":"B. Calle Ysern de la","year":"2007","unstructured":"de la Calle Ysern, B., Gonz\u00e1lez-Vera, P.: Rational quadrature formulae on the unit circle with arbitrary poles. Numer. Math. 107, 559\u2013587 (2007)","journal-title":"Numer. Math."},{"issue":"252","key":"9273_CR14","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1090\/S0025-5718-05-01763-1","volume":"74","author":"C. D\u00edaz-Mendoza","year":"2005","unstructured":"D\u00edaz-Mendoza, C., Gonz\u00e1lez-Vera, P., Jim\u00e9nez-P\u00e1iz, M.: Strong Stieltjes distributions and orthogonal Laurent polynomials with applications to quadratures and Pad\u00e9 approximation. Math. Comp. 74(252), 1843\u20131870 (2005)","journal-title":"Math. Comp."},{"key":"9273_CR15","doi-asserted-by":"crossref","unstructured":"D\u00edaz-Mendoza, C., Gonz\u00e1lez-Vera, P., Jim\u00e9nez-P\u00e1iz, M., Orive, R.: On certain symmetric strong distributions, two point Pad\u00e9 approximation and relate quadrature. Appl. Numer. Math. (2009, to appear)","DOI":"10.1016\/j.apnum.2009.03.003"},{"key":"9273_CR16","volume-title":"Tables of Integral Transforms, vol. I.","author":"A. Erd\u00e9lyi","year":"1954","unstructured":"Erd\u00e9lyi, A.: Tables of Integral Transforms, vol. I. McGraw-Hill, New York (1954)"},{"issue":"1","key":"9273_CR17","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1590\/S0103-97332003000100014","volume":"33","author":"D. Galetti","year":"2003","unstructured":"Galetti, D.: A realization of the q-deformed harmonic oscillator: Rogers-Szeg\u0151 and Stieltjes-Wigert polynomials. Braz. J. Phys. 33(1), 148\u2013157 (2003)","journal-title":"Braz. J. Phys."},{"key":"9273_CR18","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF02124749","volume":"5","author":"P. Gonz\u00e1lez-Vera","year":"1996","unstructured":"Gonz\u00e1lez-Vera, P., Nj\u00e5stad, O., Santos-Le\u00f3n, J.C.: Some results about numerical quadrature on the unit circle. Adv. Comp. Math. 5, 297\u2013328 (1996)","journal-title":"Adv. Comp. Math."},{"key":"9273_CR19","first-page":"16","volume-title":"Numer. Meth. Lin. Alg.","author":"W.B. Gragg","year":"1982","unstructured":"Gragg, W.B.: Positive definite Toeplitz matrices, the Arnoldi process for isometric operators and Gaussian quadrature on the unit circle. In: Nicholaev, E.S. (ed.) Numer. Meth. Lin. Alg., pp. 16\u201332. Moscow University Press, Moscow (1982) (in Russian)"},{"key":"9273_CR20","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0377-0427(93)90294-L","volume":"46","author":"W.B. Gragg","year":"1993","unstructured":"Gragg, W.B.: Positive definite Toeplitz matrices, the Arnoldi process for isometric operators and Gaussian quadrature on the unit circle. J. Comput. Appl. Math. 46, 183\u2013198 (1993) (This is a slightly revised version of [19])","journal-title":"J. Comput. Appl. Math."},{"key":"9273_CR21","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1112\/blms\/21.2.113","volume":"21","author":"W.B. Jones","year":"1989","unstructured":"Jones, W.B., Nj\u00e5stad, O., Thron, W.J.: Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle. Bull. Lond. Math. Soc. 21, 113\u2013152 (1989)","journal-title":"Bull. Lond. Math. Soc."},{"issue":"2","key":"9273_CR22","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1090\/S0002-9947-1980-0580900-4","volume":"261","author":"W.B. Jones","year":"1980","unstructured":"Jones, W.B., Thron, W.J., Waadeland, H.: A strong Stieltjes moment problem. Trans. Am. Math. Soc. 261(2), 503\u2013528 (1980)","journal-title":"Trans. Am. Math. Soc."},{"key":"9273_CR23","first-page":"325","volume-title":"Int. Series Numer. Math., vol. 119","author":"W.B. Jones","year":"1994","unstructured":"Jones, W.B., Waadeland, H.: Bounds for remainder terms in Szeg\u0151 quadrature on the unit circle. Approx. Comp. In: Zahar, R.V.M. (ed.) Int. Series Numer. Math., vol. 119, pp. 325\u2013346. Birkha\u030buser, Basel (1994)"},{"key":"9273_CR24","volume-title":"Analytic Function Theory, vol. II","author":"E. Hille","year":"1962","unstructured":"Hille, E.: Analytic Function Theory, vol. II. Ginn, New York (1962)"},{"issue":"5","key":"9273_CR25","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1023\/B:NUMA.0000016604.14688.21","volume":"3","author":"Q.H. Hou","year":"2004","unstructured":"Hou, Q.H., Lascoux, A., Mu, Y.P.: Continued fractions for Rogers-Szeg\u0151 polynomials. Numer. Algor. 3(5), 81\u201390 (2004)","journal-title":"Numer. Algor."},{"issue":"2","key":"9273_CR26","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/BF01203418","volume":"11","author":"G. L\u00f3pez-Lagomasino","year":"1995","unstructured":"L\u00f3pez-Lagomasino, G., Mart\u00ednez-Finkelshtein, A.: Rate of convergence of two point Pad\u00e9 approximants and logarithmic asymptotic of Laurent-type orthogonal polynomials. Constr. Approx. 11(2), 255\u2013286 (1995)","journal-title":"Constr. Approx."},{"key":"9273_CR27","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0377-0427(99)00110-7","volume":"108","author":"J.C. Santos-Le\u00f3n","year":"1999","unstructured":"Santos-Le\u00f3n, J.C.: Product rules on the unit circle with uniformly distributed nodes. Error bounds for analytic functions. J. Comp. Appl. Math. 108, 195\u2013208 (1999)","journal-title":"J. Comp. Appl. Math."},{"key":"9273_CR28","volume-title":"Amer. Math. Soc. Coll. Publ., vol. 54.1","author":"B. Simon","year":"2005","unstructured":"Simon, B.: Orthogonal polynomials on the unit circle, part 1: classical theory. In: Amer. Math. Soc. Coll. Publ., vol. 54.1. American Mathematical Society, Providence (2005)"},{"issue":"1","key":"9273_CR29","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1006\/jmaa.1995.1227","volume":"193","author":"A. Sri Ranga","year":"1995","unstructured":"Sri Ranga, A., de Andrade, E.X.L., McCabe, J.H.: Some consequences of a symmetriy in strong distributions. L. Math. Anal. Appl. 193(1), 158\u2013168 (1995)","journal-title":"L. Math. Anal. Appl."},{"key":"9273_CR30","first-page":"255","volume":"8","author":"G. Szeg\u0151","year":"1963","unstructured":"Szeg\u0151, G.: On bi-orthogonal systems of trigonometric polynomials. Magyar Tud. Akad. Kutat\u00f3 Int. K\u00f6zl 8, 255\u2013273 (1963)","journal-title":"Magyar Tud. Akad. Kutat\u00f3 Int. K\u00f6zl"},{"key":"9273_CR31","volume-title":"Amer. Math. Soc. Coll. Publ., vol. 23.","author":"G. Szeg\u0151","year":"1975","unstructured":"Szeg\u0151, G.: Orthogonal polynomials. In: Amer. Math. Soc. Coll. Publ., vol. 23. American Mathematical Society, Providence (1975)"},{"key":"9273_CR32","unstructured":"Turetzkii, A.H.: On quadrature formulae that are exact for trigomometric polynomials. East J. Approx. 11, 337\u2013359 (translation in English from Uchenye Zapiski, Vypusk 1(149), Seria Math. Theory of Functions, Collection of papers, Izdatel\u2019stvo Belgosuniversiteta imeni V.I. Lenina, Minsk (1959), 31\u201354) (2005)"},{"key":"9273_CR33","first-page":"479","volume-title":"IMACS J. Comp. Appl. Math.","author":"H. Waadeland","year":"1992","unstructured":"Waadeland, H.: A Szeg\u0151 quadrature formula for the Poisson integral. In: Brezinski, C., Kulish, U. (eds.) IMACS J. Comp. Appl. Math., pp. 479\u2013486. Elsevier Science (North-Holland), Amsterdam (1992)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-009-9273-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-009-9273-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-009-9273-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,2]],"date-time":"2021-10-02T07:09:07Z","timestamp":1633158547000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-009-9273-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,25]]},"references-count":33,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,11]]}},"alternative-id":["9273"],"URL":"https:\/\/doi.org\/10.1007\/s11075-009-9273-4","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2,25]]}}}