{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T12:35:57Z","timestamp":1765888557840,"version":"3.46.0"},"reference-count":28,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T00:00:00Z","timestamp":1614643200000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T00:00:00Z","timestamp":1614643200000},"content-version":"tdm","delay-in-days":1,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["IF\/00069\/2015 PTDC\/MAT-PUR\/30234\/2017"],"award-info":[{"award-number":["IF\/00069\/2015 PTDC\/MAT-PUR\/30234\/2017"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2021,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We study the roots of the generalised Hermite polynomials\n                    <jats:italic>H<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>m<\/jats:italic>\n                      ,\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    when both\n                    <jats:italic>m<\/jats:italic>\n                    and\n                    <jats:italic>n<\/jats:italic>\n                    are large. We prove that the roots, when appropriately rescaled, densely fill a bounded quadrilateral region, called the elliptic region, and organise themselves on a deformed rectangular grid, as was numerically observed by Clarkson. We describe the elliptic region and the deformed grid in terms of elliptic integrals and their degenerations.\n                  <\/jats:p>","DOI":"10.1088\/1361-6544\/abdd93","type":"journal-article","created":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T03:28:35Z","timestamp":1615260515000},"page":"1663-1732","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Roots of generalised Hermite polynomials when both parameters are large"],"prefix":"10.1088","volume":"34","author":[{"given":"Davide","family":"Masoero","sequence":"first","affiliation":[]},{"given":"Pieter","family":"Roffelsen","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2021,3,2]]},"reference":[{"year":"1983","author":"A\u012dzenberg","key":"nonabdd93bib1","type":"book"},{"key":"nonabdd93bib2","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s13324-011-0012-3","type":"journal-article","article-title":"Boutroux curves with external field: equilibrium measures without a variational problem","volume":"1","author":"Bertola","year":"2011","journal-title":"Anal. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2019-09-01","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-01-19","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-03-02","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}