{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T18:44:07Z","timestamp":1758393847167,"version":"3.37.3"},"reference-count":0,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[1994,12,15]],"date-time":"1994-12-15T00:00:00Z","timestamp":787449600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004062","name":"Junta Nacional de Investiga\u00e7\u00e3o Cient\u00edfica e Tecnol\u00f3gica","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004062","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[1996,1]]},"abstract":"<jats:p>Given a sequence of monic orthogonal polynomials (MOPS), {<jats:italic>P<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>}, with respect\nto a quasi\u2010definite linear functional <jats:italic>u<\/jats:italic>, we find necessary and sufficient conditions on the parameters\n<jats:italic>a<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> and <jats:italic>b<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>\n for the sequence\n<jats:disp-formula>\n\n<jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" position=\"anchor\" xlink:href=\"graphic\/ijmm657910-math-0001.png\"><jats:alt-text>urn:x-wiley:01611712:media:ijmm657910:ijmm657910-math-0001<\/jats:alt-text><\/jats:graphic>\n<\/jats:disp-formula>\n\nto be orthogonal. In particular, we can find explicitly the linear functional <jats:italic>v<\/jats:italic> such that the new\nsequence is the corresponding family of orthogonal polynomials. Some applications for Hermite\nand Tchebychev orthogonal polynomials of second kind are obtained.<\/jats:p><jats:p>We also solve a problem of this type for orthogonal polynomials with respect to a Hermitian\nlinear functional.<\/jats:p>","DOI":"10.1155\/s0161171296000919","type":"journal-article","created":{"date-parts":[[2002,9,16]],"date-time":"2002-09-16T12:00:16Z","timestamp":1032177616000},"page":"643-656","source":"Crossref","is-referenced-by-count":21,"title":["Generating new classes of orthogonal polynomials"],"prefix":"10.1155","volume":"19","author":[{"given":"Am\u00edlcar","family":"Branquinho","sequence":"first","affiliation":[]},{"given":"Francisco","family":"Marcell\u00e1n","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[1994,12,15]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/1996\/657910.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171296000919","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T13:52:10Z","timestamp":1719496330000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171296000919"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,12,15]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["10.1155\/S0161171296000919"],"URL":"https:\/\/doi.org\/10.1155\/s0161171296000919","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[1994,12,15]]}}}