{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T16:41:36Z","timestamp":1770741696137,"version":"3.49.0"},"reference-count":18,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper addresses two primary objectives in the realm of classical multiple orthogonal polynomials with an arbitrary number of weights. Firstly, it establishes new and explicit hypergeometric expressions for type I Hahn multiple orthogonal polynomials. Secondly, applying the residue theorem and the Mellin transform, the paper derives contour integral representations for several families of orthogonal polynomials. Specifically, it presents contour integral formulas for both type I and type II multiple orthogonal polynomials in the Laguerre of the first kind, Jacobi\u2013Pi\u00f1eiro, and Hahn families. The evaluation of these integrals leads to explicit hypergeometric representations.<\/jats:p>","DOI":"10.1093\/imrn\/rnaf168","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T15:35:53Z","timestamp":1751038553000},"source":"Crossref","is-referenced-by-count":2,"title":["Integral and Hypergeometric Representations for Multiple Orthogonal Polynomials"],"prefix":"10.1093","volume":"2025","author":[{"given":"Am\u00edlcar","family":"Branquinho","sequence":"first","affiliation":[{"name":"CMUC, Departamento de Matem\u00e1tica, Universidade de Coimbra , Largo D. Dinis, 3000-143 Coimbra, Portugal"}]},{"given":"Juan E F","family":"D\u00edaz","sequence":"additional","affiliation":[{"name":"CIDMA, Departamento de Matem\u00e1tica, Universidade de Aveiro , 3810-193 Aveiro, Portugal"}]},{"given":"Ana","family":"Foulqui\u00e9-Moreno","sequence":"additional","affiliation":[{"name":"CIDMA, Departamento de Matem\u00e1tica, Universidade de Aveiro , 3810-193 Aveiro, Portugal"}]},{"given":"Manuel","family":"Ma\u00f1as","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Te\u00f3rica, Universidad Complutense de Madrid , 28040 Madrid, Spain"}]},{"given":"Thomas","family":"Wolfs","sequence":"additional","affiliation":[{"name":"Department of Mathematics, KU Leuven , 3001 Leuven, Belgium"}]}],"member":"286","published-online":{"date-parts":[[2025,6,19]]},"reference":[{"key":"2025062711362009200_ref1","doi-asserted-by":"publisher","first-page":"1451","DOI":"10.1016\/j.aim.2011.03.008","article-title":"Multiple orthogonal polynomials of mixed type: Gauss\u2013Borel factorization and the multi-component 2D Toda hierarchy","volume":"227","author":"\u00c1lvarez-Fern\u00e1ndez","year":"2011","journal-title":"Adv. Math."},{"key":"2025062711362009200_ref2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107325937","volume-title":"Special Functions","author":"Andrews","year":"1999"},{"key":"2025062711362009200_ref3","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0377-0427(02)00597-6","article-title":"Some discrete multiple orthogonal polynomials","volume":"153","author":"Arvesu","year":"2003","journal-title":"J. Comput. Appl. Math."},{"key":"2025062711362009200_ref4","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.jat.2004.12.001","article-title":"Multiple Wilson and Jacobi\u2013Pi\u00f1eiro polynomials","volume":"132","author":"Beckerman","year":"2005","journal-title":"J. Approx. Theory"},{"key":"2025062711362009200_ref5","doi-asserted-by":"publisher","first-page":"e70033","DOI":"10.1111\/sapm.70033","article-title":"Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation","volume":"154","author":"Branquinho","year":"2025","journal-title":"Stud. Appl. Math."},{"key":"2025062711362009200_ref6","doi-asserted-by":"publisher","first-page":"1277471","DOI":"10.1016\/j.jmaa.2023.127471","article-title":"Hahn multiple orthogonal polynomials of type I: hypergeometric expressions","volume":"528","author":"Branquinho","year":"2023","journal-title":"J. Math. Anal. Appl."},{"key":"2025062711362009200_ref7","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1090\/bproc\/225","article-title":"Hypergeometric expressions for type I Jacobi\u2013Pi\u00f1eiro orthogonal polynomials with arbitrary number of weights","volume":"11","author":"Branquinho","year":"2024","journal-title":"Proc. Am. Math. Soc. B"},{"key":"2025062711362009200_ref8","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107325982","volume-title":"Classical and Quantum Orthogonal Polynomials in One Variable","author":"Ismail","year":"2005"},{"key":"2025062711362009200_ref9","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1080\/10652469.2018.1526793","article-title":"Extensions of Karlsson\u2013Minton summation theorem and some consequences of the first Miller\u2013Paris transformation","volume":"29","author":"Karp","year":"2018","journal-title":"Integral Transforms Spec. Funct."},{"key":"2025062711362009200_ref10","volume-title":"The Art of Computer Programming. Volume 3. Sorting and Searching","author":"Knuth","year":"1973"},{"key":"2025062711362009200_ref11","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/092","volume-title":"Rational Approximations and Orthogonality","author":"Nikishin","year":"1991"},{"key":"2025062711362009200_ref12","author":"NIST Digital Library of Mathematical Functions"},{"key":"2025062711362009200_ref13","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1080\/00150517.1994.12429189","article-title":"Some information about the binomial transform","volume":"32","author":"Prodinger","year":"1994","journal-title":"Fibonacci Q."},{"issue":"2","key":"2025062711362009200_ref14","first-page":"473","article-title":"Certain reduction and transformation formulas for the Kamp\u00e9 de F\u00e9riet function","volume":"37","author":"Rakha","year":"2022","journal-title":"Commun. Korean Math. Soc."},{"key":"2025062711362009200_ref15","volume-title":"Generalized Hypergeometric Functions","author":"Slater","year":"2008"},{"key":"2025062711362009200_ref16","volume-title":"Multiple Gaussian Hypergeometric Series, Ellis Horwood Limited","author":"Srivastava","year":"1985"},{"key":"2025062711362009200_ref17","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1111\/sapm.12608","article-title":"Multiple orthogonal polynomials associated with the exponential integral","volume":"151","author":"Van Assche","year":"2023","journal-title":"Stud. Appl. Math."},{"key":"2025062711362009200_ref18","doi-asserted-by":"publisher","first-page":"102709","DOI":"10.1016\/j.aam.2024.102709","article-title":"Applications of multiple orthogonal polynomials with hypergeometric moment generating functions","volume":"158","author":"Wolfs","year":"2024","journal-title":"Adv. Appl. Math."}],"container-title":["International Mathematics Research Notices"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/imrn\/article-pdf\/2025\/12\/rnaf168\/63532420\/rnaf168.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/imrn\/article-pdf\/2025\/12\/rnaf168\/63532420\/rnaf168.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T15:36:31Z","timestamp":1751038591000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imrn\/article\/doi\/10.1093\/imrn\/rnaf168\/8169765"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6]]},"references-count":18,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2025,6,23]]}},"URL":"https:\/\/doi.org\/10.1093\/imrn\/rnaf168","relation":{},"ISSN":["1073-7928","1687-0247"],"issn-type":[{"value":"1073-7928","type":"print"},{"value":"1687-0247","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,6]]},"published":{"date-parts":[[2025,6]]},"article-number":"rnaf168"}}