{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T12:30:53Z","timestamp":1777984253422,"version":"3.51.4"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"10","license":[{"start":{"date-parts":[[2004,6,10]],"date-time":"2004-06-10T00:00:00Z","timestamp":1086825600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Trans. Amer. Math. Soc."],"abstract":"<p>\n                    A new set of special functions, which has a wide range of applications from number theory to integrability of nonlinear dynamical systems, is described. We study multiple orthogonal polynomials with respect to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p greater-than 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">p &gt; 1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    weights satisfying Pearson\u2019s equation. In particular, we give a classification of multiple orthogonal polynomials with respect to classical weights, which is based on properties of the corresponding Rodrigues operators. We show that the multiple orthogonal polynomials in our classification satisfy a linear differential equation of order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p plus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">p+1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We also obtain explicit formulas and recurrence relations for these polynomials.\n                  <\/p>","DOI":"10.1090\/s0002-9947-03-03330-0","type":"journal-article","created":{"date-parts":[[2003,7,9]],"date-time":"2003-07-09T17:31:00Z","timestamp":1057771860000},"page":"3887-3914","source":"Crossref","is-referenced-by-count":118,"special_numbering":"821","title":["Multiple orthogonal polynomials for classical weights"],"prefix":"10.1090","volume":"355","author":[{"given":"A.","family":"Aptekarev","sequence":"first","affiliation":[]},{"given":"A.","family":"Branquinho","sequence":"additional","affiliation":[]},{"given":"W.","family":"Van Assche","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2003,6,10]]},"reference":[{"issue":"1-2","key":"1","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/S0377-0427(98)00175-7","article-title":"Multiple orthogonal polynomials","volume":"99","author":"Aptekarev, A. I.","year":"1998","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"52","key":"2","first-page":"3","article-title":"Complex rational approximation and difference operators","author":"Aptekarev, A.","year":"1998","journal-title":"Rend. Circ. Mat. Palermo (2) Suppl.","ISSN":"https:\/\/id.crossref.org\/issn\/1592-9531","issn-type":"print"},{"issue":"4","key":"3","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s003650010004","article-title":"The genetic sums\u2019 representation for the moments of a system of Stieltjes functions and its application","volume":"16","author":"Aptekarev, A.","year":"2000","journal-title":"Constr. Approx.","ISSN":"https:\/\/id.crossref.org\/issn\/0176-4276","issn-type":"print"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1006\/jath.1996.3074","article-title":"Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials","volume":"90","author":"Aptekarev, A. I.","year":"1997","journal-title":"J. Approx. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9045","issn-type":"print"},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1112\/blms\/11.3.268","article-title":"A note on the irrationality of \ud835\udf01(2) and \ud835\udf01(3)","volume":"11","author":"Beukers, F.","year":"1979","journal-title":"Bull. London Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"key":"6","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0793-1","volume-title":"Polynomials and polynomial inequalities","volume":"161","author":"Borwein, Peter","year":"1995","ISBN":"https:\/\/id.crossref.org\/isbn\/0387945091"},{"issue":"1","key":"7","first-page":"1","article-title":"A note on semi-classical orthogonal polynomials","volume":"3","author":"Branquinho, Am\u00edlcar","year":"1996","journal-title":"Bull. Belg. Math. Soc. Simon Stevin","ISSN":"https:\/\/id.crossref.org\/issn\/1370-1444","issn-type":"print"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/BF00998681","article-title":"Classical orthogonal polynomials: a functional approach","volume":"34","author":"Marcell\u00e1n, F.","year":"1994","journal-title":"Acta Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0167-8019","issn-type":"print"},{"issue":"6","key":"9","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1070\/SM1995v082n01ABEH003558","article-title":"Hermite-Pad\u00e9 approximants and spectral analysis of nonsymmetric operators","volume":"185","author":"Kalyagin, V. A.","year":"1994","journal-title":"Mat. Sb.","ISSN":"https:\/\/id.crossref.org\/issn\/0368-8666","issn-type":"print"},{"issue":"1-3","key":"10","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/0377-0427(95)00109-3","article-title":"The operator moment problem, vector continued fractions and an explicit form of the Favard theorem for vector orthogonal polynomials","volume":"65","author":"Kaliaguine, V.","year":"1995","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"2","key":"11","first-page":"67","article-title":"On simultaneous approximations for some collection of Markov functions","author":"Pine\u012dro Dias, L. R.","year":"1987","journal-title":"Vestnik Moskov. Univ. Ser. I Mat. Mekh.","ISSN":"https:\/\/id.crossref.org\/issn\/0579-9368","issn-type":"print"},{"key":"12","series-title":"Translations of Mathematical Monographs","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/092","volume-title":"Rational approximations and orthogonality","volume":"92","author":"Nikishin, E. M.","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0821845454"},{"issue":"11","key":"13","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/BF01097274","article-title":"Generalization of classical orthogonal polynomials and convergence of simultaneous Pad\u00e9 approximants","author":"Sorokin, V. N.","year":"1986","journal-title":"Trudy Sem. Petrovsk.","ISSN":"https:\/\/id.crossref.org\/issn\/0321-2971","issn-type":"print"},{"issue":"5","key":"14","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1007\/BF00974495","article-title":"Simultaneous Pad\u00e9 approximations of functions of Stieltjes type","volume":"31","author":"Sorokin, V. N.","year":"1990","journal-title":"Sibirsk. Mat. Zh.","ISSN":"https:\/\/id.crossref.org\/issn\/0037-4474","issn-type":"print"},{"issue":"2","key":"15","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1070\/RM1994v049n02ABEH002229","article-title":"Hermite-Pad\u00e9 approximants for Nikishin systems and the irrationality of \ud835\udf01(3)","volume":"49","author":"Sorokin, V. N.","year":"1994","journal-title":"Uspekhi Mat. Nauk","ISSN":"https:\/\/id.crossref.org\/issn\/0042-1316","issn-type":"print"},{"key":"16","isbn-type":"print","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1090\/conm\/236\/03504","article-title":"Multiple orthogonal polynomials, irrationality and transcendence","author":"Van Assche, Walter","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0821812009"},{"key":"17","isbn-type":"print","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1090\/crmp\/025\/40","article-title":"Nonsymmetric linear difference equations for multiple orthogonal polynomials","author":"Van Assche, Walter","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/0821821288"},{"issue":"1-2","key":"18","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/S0377-0427(00)00503-3","article-title":"Some classical multiple orthogonal polynomials","volume":"127","author":"Van Assche, Walter","year":"2001","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"}],"container-title":["Transactions of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/tran\/2003-355-10\/S0002-9947-03-03330-0\/S0002-9947-03-03330-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/tran\/2003-355-10\/S0002-9947-03-03330-0\/S0002-9947-03-03330-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T04:48:16Z","timestamp":1775796496000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/tran\/2003-355-10\/S0002-9947-03-03330-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,6,10]]},"references-count":18,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2003,10]]}},"alternative-id":["S0002-9947-03-03330-0"],"URL":"https:\/\/doi.org\/10.1090\/s0002-9947-03-03330-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6850","0002-9947"],"issn-type":[{"value":"1088-6850","type":"electronic"},{"value":"0002-9947","type":"print"}],"subject":[],"published":{"date-parts":[[2003,6,10]]}}}