{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:46:41Z","timestamp":1777448801198,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2010,2,1]],"date-time":"2010-02-01T00:00:00Z","timestamp":1264982400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2010,2]]},"abstract":"<jats:p>We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler\u2013Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.<\/jats:p>","DOI":"10.3233\/asy-2009-0961","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:09:30Z","timestamp":1575054570000},"page":"103-117","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotics for a generalization of Hermite polynomials"],"prefix":"10.1177","volume":"66","author":[{"given":"Manuel","family":"Alfaro","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas and IUMA, Univ. de Zaragoza, Zaragoza, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ana","family":"Pe\u00f1a","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas and IUMA, Univ. de Zaragoza, Zaragoza, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. Luisa","family":"Rezola","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas and IUMA, Univ. de Zaragoza, Zaragoza, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Jos\u00e9","family":"Moreno-Balc\u00e1zar","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica y Matem\u00e1tica Aplicada, Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Univ. de Almer\u00eda, Almer\u00eda, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2010,2,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2009-0961","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2009-0961","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:00Z","timestamp":1777379940000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2009-0961"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,2]]}},"alternative-id":["10.3233\/ASY-2009-0961"],"URL":"https:\/\/doi.org\/10.3233\/asy-2009-0961","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2]]}}}