{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:24:47Z","timestamp":1773800687018,"version":"3.50.1"},"reference-count":61,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T00:00:00Z","timestamp":1649289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>In this paper, the Riemann\u2013Hilbert problem, with a jump supported on an appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of the corresponding matrix biorthogonal polynomials associated with Laguerre type matrices of weights\u2014which are constructed in terms of a given matrix Pearson equation. First and second order differential systems for the fundamental matrix, solution of the mentioned Riemann\u2013Hilbert problem, are derived. An explicit and general example is presented to illustrate the theoretical results of the work. The non-Abelian extensions of a family of discrete Painlev\u00e9 IV equations are discussed.<\/jats:p>","DOI":"10.3390\/math10081205","type":"journal-article","created":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T21:08:22Z","timestamp":1649365702000},"page":"1205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Riemann\u2013Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: The Matrix Discrete Painlev\u00e9 IV"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4685-1583","authenticated-orcid":false,"given":"Am\u00edlcar","family":"Branquinho","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade de Coimbra, 3001-454 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5097-950X","authenticated-orcid":false,"given":"Ana Foulqui\u00e9","family":"Moreno","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade de Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2398-990X","authenticated-orcid":false,"given":"Assil","family":"Fradi","sequence":"additional","affiliation":[{"name":"Mathematical Physics Special Functions and Applications Laboratory, The Higher School of Sciences and Technology of Hammam Sousse, University of Sousse, Sousse 4002, Tunisia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3764-5737","authenticated-orcid":false,"given":"Manuel","family":"Ma\u00f1as","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Te\u00f3rica, Universidad Complutense de Madrid, 28040 Madrid, Spain"},{"name":"Instituto de Ciencias Matematicas (ICMAT), Campus de Cantoblanco UAM, 28049 Madrid, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,7]]},"reference":[{"key":"ref_1","first-page":"125","article-title":"Infinite J-matrices and a matrix moment problem","volume":"69","author":"Krein","year":"1949","journal-title":"Dokl. 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