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Amer. Math. Soc."],"abstract":"<p>\n                    We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann\u2013Hilbert problem we can derive first and second order differential-difference relations that these matrix orthogonal polynomials and the second kind functions associated to them verify. For the corresponding matrix recurrence coefficients, non-Abelian extensions of a family of discrete Painlev\u00e9 d-P\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"Subscript upper I upper V\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi\/>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>I<\/mml:mi>\n                              <mml:mi>V<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">_{IV}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    equations are obtained for the three term recurrence relation coefficients.\n                  <\/p>","DOI":"10.1090\/proc\/16431","type":"journal-article","created":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T10:59:01Z","timestamp":1675249141000},"page":"193-208","source":"Crossref","is-referenced-by-count":5,"special_numbering":"775","title":["Matrix Jacobi biorthogonal polynomials via Riemann\u2013Hilbert problem"],"prefix":"10.1090","volume":"152","author":[{"given":"Am\u00edlcar","family":"Branquinho","sequence":"first","affiliation":[]},{"given":"Ana","family":"Foulqui\u00e9-Moreno","sequence":"additional","affiliation":[]},{"given":"Assil","family":"Fradi","sequence":"additional","affiliation":[]},{"given":"Manuel","family":"Ma\u00f1as","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,10,6]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"1285","DOI":"10.1093\/imrn\/rnw027","article-title":"Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy","author":"\u00c1lvarez-Fern\u00e1ndez, Carlos","year":"2017","journal-title":"Int. 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