{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T18:23:05Z","timestamp":1740162185521,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2019,2,7]],"date-time":"2019-02-07T00:00:00Z","timestamp":1549497600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["287523"],"award-info":[{"award-number":["287523"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006527","name":"Direcci\u00f3n General de Investigaci\u00f3n Cient\u00edfica y T\u00e9cnica","doi-asserted-by":"publisher","award":["MTM2015-65888-C4-2-P","MTM2015-65888-C4-2-P"],"award-info":[{"award-number":["MTM2015-65888-C4-2-P","MTM2015-65888-C4-2-P"]}],"id":[{"id":"10.13039\/501100006527","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006527","name":"Direcci\u00f3n General de Investigaci\u00f3n Cient\u00edfica y T\u00e9cnica","doi-asserted-by":"publisher","award":["MTM2015-65888-C4-2-P"],"award-info":[{"award-number":["MTM2015-65888-C4-2-P"]}],"id":[{"id":"10.13039\/501100006527","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Afr. Mat."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s13370-019-00663-6","type":"journal-article","created":{"date-parts":[[2019,2,7]],"date-time":"2019-02-07T11:00:47Z","timestamp":1549537247000},"page":"505-528","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On Freud\u2013Sobolev type orthogonal polynomials"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2569-186X","authenticated-orcid":false,"given":"Luis E.","family":"Garza","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6802-3303","authenticated-orcid":false,"given":"Edmundo J.","family":"Huertas","sequence":"additional","affiliation":[]},{"given":"Francisco","family":"Marcell\u00e1n","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,2,7]]},"reference":[{"issue":"3","key":"663_CR1","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1137\/0523038","volume":"23","author":"M Alfaro","year":"1992","unstructured":"Alfaro, M., Marcell\u00e1n, F., Rezola, M.L., Ronveaux, A.: On orthogonal polynomials of Sobolev type: algebraic properties and zeros. SIAM J. Math. Anal. 23(3), 737\u2013757 (1992)","journal-title":"SIAM J. Math. Anal."},{"key":"663_CR2","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1006\/jath.1995.1121","volume":"83","author":"M Alfaro","year":"1995","unstructured":"Alfaro, M., Marcell\u00e1n, F., Rezola, M.L., Ronveaux, A.: Sobolev type: the nondiagonal case. J. Approx. Theory 83, 266\u2013287 (1995)","journal-title":"J. Approx. Theory"},{"key":"663_CR3","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.amc.2016.01.048","volume":"281","author":"A Arceo","year":"2016","unstructured":"Arceo, A., Huertas, E.J., Marcell\u00e1n, F.: On polynomials associated with an Uvarov modification of a quartic potential Freud-like weight. Appl. Math. Comput. 281, 102\u2013120 (2016)","journal-title":"Appl. Math. Comput."},{"key":"663_CR4","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/0021-9045(90)90104-X","volume":"63","author":"S Bonan","year":"1990","unstructured":"Bonan, S., Clark, D.: Estimates of the Hermite and Freud polynomials. J. Approx. Theory 63, 210\u2013224 (1990)","journal-title":"J. Approx. Theory"},{"key":"663_CR5","unstructured":"Bouali, M.: Sobolev Freud polynomials, arXiv:1502.06500 [math.CA] (2015)"},{"key":"663_CR6","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/S0377-0427(01)00499-X","volume":"143","author":"CF Bracciali","year":"2002","unstructured":"Bracciali, C.F., Dimitrov, D.K., Sri Ranga, A.: Chain sequences and symmetric generalized orthogonal polynomials. J. Comput. Appl. Math. 143, 95\u2013106 (2002)","journal-title":"J. Comput. Appl. Math."},{"key":"663_CR7","volume-title":"An Introduction to Orthogonal Polynomials","author":"TS Chihara","year":"1978","unstructured":"Chihara, T.S.: An Introduction to Orthogonal Polynomials. Gordon and Breach, New York (1978)"},{"key":"663_CR8","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1111\/sapm.12105","volume":"136","author":"PA Clarkson","year":"2016","unstructured":"Clarkson, P.A., Jordaan, K., Kelil, A.: A generalized Freud weight. Stud. Appl. Math. 136, 288\u2013320 (2016)","journal-title":"Stud. Appl. Math."},{"key":"663_CR9","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/j.jat.2017.10.001","volume":"225","author":"PA Clarkson","year":"2018","unstructured":"Clarkson, P.A., Jordaan, K.: Properties of generalized Freud polynomials. J. Approx. Theory 225, 148\u2013175 (2018)","journal-title":"J. Approx. Theory"},{"key":"663_CR10","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.apnum.2009.12.004","volume":"60","author":"DK Dimitrov","year":"2010","unstructured":"Dimitrov, D.K., Mello, M.V., Rafaeli, F.R.: Monotonicity of zeros of Jacobi\u2013Sobolev type orthogonal polynomials. Appl. Numer. Math. 60, 263\u2013276 (2010)","journal-title":"Appl. Numer. Math."},{"issue":"10","key":"663_CR11","doi-asserted-by":"publisher","first-page":"2211","DOI":"10.1088\/0951-7715\/19\/10\/001","volume":"19","author":"M Duits","year":"2006","unstructured":"Duits, M., Kuijlaars, A.B.J.: Painlev\u00e9 I asymptotics for orthogonal polynomials with respect to a varying quartic weight. Nonlinearity 19(10), 2211\u20132245 (2006)","journal-title":"Nonlinearity"},{"key":"663_CR12","doi-asserted-by":"publisher","first-page":"205201","DOI":"10.1088\/1751-8113\/45\/20\/205201","volume":"45","author":"G Filipuk","year":"2012","unstructured":"Filipuk, G., Van Asche, W., Zhang, L.: The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlev\u00e9 equation. J. Phys. A Math. Theor. 45, 205201 (2012)","journal-title":"J. Phys. A Math. Theor."},{"key":"663_CR13","first-page":"37","volume":"19","author":"A Garrido","year":"2005","unstructured":"Garrido, A., Arves\u00fa, J., Marcell\u00e1n, F.: An electrostatic interpretation of the zeros of the Freud-type orthogonal polynomials. Electron. Trans. Numer. Anal. 19, 37\u201347 (2005)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"663_CR14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325982","volume-title":"Classical and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of Mathematics and its Applications","author":"MEH Ismail","year":"2005","unstructured":"Ismail, M.E.H.: Classical and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of Mathematics and its Applications, vol. 98. Cambridge University Press, Cambridge (2005)"},{"key":"663_CR15","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/0021-9045(83)90154-5","volume":"38","author":"JS Lew","year":"1983","unstructured":"Lew, J.S., Quarles Jr., D.A.: Nonnegative solutions of a nonlinear recurrence. J. Approx. Theory 38, 357\u2013379 (1983)","journal-title":"J. Approx. Theory"},{"issue":"7","key":"663_CR16","first-page":"455","volume":"12","author":"F Marcell\u00e1n","year":"1992","unstructured":"Marcell\u00e1n, F., P\u00e9rez, T.E., Pi\u00f1ar, M.A.: On zeros of Sobolev-type orthogonal polynomials. Rend. Mat. Appl. 12(7), 455\u2013473 (1992)","journal-title":"Rend. Mat. Appl."},{"issue":"2","key":"663_CR17","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1016\/j.cam.2006.10.020","volume":"207","author":"F Marcell\u00e1n","year":"2007","unstructured":"Marcell\u00e1n, F., Mart\u00ednez-Finkelshtein, A., Mart \u00ednez-Gonz\u00e1lez, P.: Electrostatic models for zeros of polynomials: old, new, and some open problems. J. Comput. Appl. Math. 207(2), 258\u2013272 (2007)","journal-title":"J. Comput. Appl. Math."},{"key":"663_CR18","unstructured":"Maroni, P.: Une th\u00e9orie alg\u00e9brique des polyn\u00f4mes orthogonaux. Application aux polyn\u00f4mes orthogonaux semi-classiques. In: Brezinski, C., et al. (eds.) Orthogonal Polynomials and Their Applications. Annals. Comput. Appl. Math. vol. 9, pp. 95\u2013130. Baltzer, Basel (1991)"},{"key":"663_CR19","first-page":"263","volume":"3","author":"P Nevai","year":"1983","unstructured":"Nevai, P.: Orthogonal polynomials associated with $$ \\exp (-x^{4})$$ exp ( - x 4 ) in second edmonton conference on approximation theory. Can. Math. Soc. Conf. Proc. 3, 263\u2013285 (1983)","journal-title":"Can. Math. Soc. Conf. Proc."},{"key":"663_CR20","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1137\/0515092","volume":"15","author":"P Nevai","year":"1984","unstructured":"Nevai, P.: Asymptotics for orthogonal polynomials associated with $$\\exp (-x^{4})$$ exp ( - x 4 ) . SIAM J. Math. Anal. 15, 1177\u20131187 (1984)","journal-title":"SIAM J. Math. Anal."},{"key":"663_CR21","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1215\/S0012-7094-39-00534-X","volume":"5","author":"J Shohat","year":"1939","unstructured":"Shohat, J.: A differential equation for orthogonal polynomials. Duke Math. J. 5, 401\u2013417 (1939)","journal-title":"Duke Math. J."},{"key":"663_CR22","unstructured":"Szeg\u0151, G.: Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ. Series, vol. 23, Amer. Math. Soc., Providence, RI (1975)"},{"key":"663_CR23","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1142\/9789812770752_0058","volume-title":"Difference Equations, Special Functions and Orthogonal Polynomials","author":"W Assche Van","year":"2007","unstructured":"Van Assche, W.: Discrete Painlev\u00e9 equations for recurrence coefficients of orthogonal polynomials. In: Elaydi, S., et al. (eds.) Difference Equations, Special Functions and Orthogonal Polynomials, pp. 687\u2013725. World Scientific, Singapore (2007)"},{"key":"663_CR24","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/S0377-0427(97)00130-1","volume":"85","author":"A Zhedanov","year":"1997","unstructured":"Zhedanov, A.: Rational spectral transformations and orthogonal polynomials. J. Comput. Appl. Math. 85, 67\u201383 (1997)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Afrika Matematika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13370-019-00663-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13370-019-00663-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13370-019-00663-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,11]],"date-time":"2022-09-11T14:33:18Z","timestamp":1662906798000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13370-019-00663-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,7]]},"references-count":24,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["663"],"URL":"https:\/\/doi.org\/10.1007\/s13370-019-00663-6","relation":{},"ISSN":["1012-9405","2190-7668"],"issn-type":[{"type":"print","value":"1012-9405"},{"type":"electronic","value":"2190-7668"}],"subject":[],"published":{"date-parts":[[2019,2,7]]},"assertion":[{"value":"26 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 February 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}