{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T08:47:22Z","timestamp":1743151642230,"version":"3.40.3"},"publisher-location":"Cham","reference-count":23,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031696459"},{"type":"electronic","value":"9783031696466"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-69646-6_10","type":"book-chapter","created":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T19:38:59Z","timestamp":1735328339000},"page":"209-231","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Differential Relations of\u00a0Functionals Associated with\u00a02-Orthogonal Eigenfunctions"],"prefix":"10.1007","author":[{"given":"T. A.","family":"Mesquita","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,12,28]]},"reference":[{"key":"10_CR1","doi-asserted-by":"publisher","unstructured":"Bochner, S.: \u00dcber Sturm-Liouvillesche Polynomsysteme. Math. Z. 29(1), 730\u2013736 (1929). https:\/\/doi.org\/10.1007\/BF01180560","DOI":"10.1007\/BF01180560"},{"key":"10_CR2","volume-title":"An Introduction to Orthogonal Polynomials, Mathematics and its Applications","author":"TS Chihara","year":"1978","unstructured":"Chihara, T.S.: An Introduction to Orthogonal Polynomials, Mathematics and its Applications, vol. 13. Gordon and Breach Science Publishers, New York-London-Paris (1978)"},{"key":"10_CR3","doi-asserted-by":"publisher","unstructured":"Coussement, J., Van\u00a0Assche, W.: Differential equations for multiple orthogonal polynomials with respect to classical weights: raising and lowering operators. J. Phys. A 39(13), 3311\u20133318 (2006). https:\/\/doi.org\/10.1088\/0305-4470\/39\/13\/010","DOI":"10.1088\/0305-4470\/39\/13\/010"},{"key":"10_CR4","doi-asserted-by":"publisher","unstructured":"Douak, K.: The relation of the $$d$$-orthogonal polynomials to the Appell polynomials. J. Comput. Appl. Math. 70(2), 279\u2013295 (1996). https:\/\/doi.org\/10.1016\/0377-0427(95)00211-1","DOI":"10.1016\/0377-0427(95)00211-1"},{"key":"10_CR5","doi-asserted-by":"publisher","unstructured":"Douak, K.: On $$2$$-orthogonal polynomials of Laguerre type. Int. J. Math. Math. Sci. 22(1), 29\u201348 (1999). https:\/\/doi.org\/10.1155\/S0161171299220297","DOI":"10.1155\/S0161171299220297"},{"key":"10_CR6","doi-asserted-by":"publisher","unstructured":"Douak, K., Maroni, P.: Les polyn\u00f4mes orthogonaux \u201cclassiques\u201d de dimension deux. Analysis 12(1-2), 71\u2013107 (1992). https:\/\/doi.org\/10.1524\/anly.1992.12.12.71","DOI":"10.1524\/anly.1992.12.12.71"},{"key":"10_CR7","doi-asserted-by":"publisher","unstructured":"Douak, K., Maroni, P.: Une caract\u00e9risation des polyn\u00f4mes $$d$$-orthogonaux \u201cclassiques\u201d. J. Approx. Theory 82(2), 177\u2013204 (1995). https:\/\/doi.org\/10.1006\/jath.1995.1074","DOI":"10.1006\/jath.1995.1074"},{"key":"10_CR8","doi-asserted-by":"publisher","unstructured":"Douak, K., Maroni, P.: On $$d$$-orthogonal Tchebychev polynomials. I. Appl. Numer. Math. 24(1), 23\u201353 (1997). https:\/\/doi.org\/10.1016\/S0168-9274(97)00006-8","DOI":"10.1016\/S0168-9274(97)00006-8"},{"key":"10_CR9","doi-asserted-by":"publisher","unstructured":"Douak, K., Maroni, P.: On a new class of 2-orthogonal polynomials, I: the recurrence relations and some properties. Integral Transforms Spec. Funct. 32(2), 134\u2013153 (2021). https:\/\/doi.org\/10.1080\/10652469.2020.1811702","DOI":"10.1080\/10652469.2020.1811702"},{"key":"10_CR10","doi-asserted-by":"crossref","unstructured":"Maroni, P.: L\u2019orthogonalit\u00e9 et les r\u00e9currences de polyn\u00f4mes d\u2019ordre sup\u00e9rieur \u00e0 deux. Ann. Fac. Sci. Toulouse Math. (5) 10(1), 105\u2013139 (1989). http:\/\/www.numdam.org\/item?id=AFST_1989_5_10_1_105_0","DOI":"10.5802\/afst.672"},{"key":"10_CR11","unstructured":"Maroni, P.: Une th\u00e9orie alg\u00e9brique des polyn\u00f4mes orthogonaux. Application aux polyn\u00f4mes orthogonaux semi-classiques. In: Brezinski, C, Gori, L., Ronveaux, A. (eds.) Orthogonal Polynomials and Their Applications (Erice, 1990), IMACS Ann. Comput. Appl. Math., vol.\u00a09, pp. 95\u2013130. Baltzer, Basel (1991)"},{"key":"10_CR12","doi-asserted-by":"publisher","unstructured":"Maroni, P.: Two-dimensional orthogonal polynomials, their associated sets and the co-recursive sets. Numer. Algorithms 3(1-4), 299\u2013311 (1992). https:\/\/doi.org\/10.1007\/BF02141938","DOI":"10.1007\/BF02141938"},{"key":"10_CR13","doi-asserted-by":"publisher","unstructured":"Maroni, P.: Variations around classical orthogonal polynomials. Connected problems. J. Comput. Appl. Math. 48(1-2), 133\u2013155 (1993). https:\/\/doi.org\/10.1016\/0377-0427(93)90319-7","DOI":"10.1016\/0377-0427(93)90319-7"},{"key":"10_CR14","doi-asserted-by":"publisher","unstructured":"Maroni, P.: Semi-classical character and finite-type relations between polynomial sequences. Appl. Numer. Math. 31(3), 295\u2013330 (1999). https:\/\/doi.org\/10.1016\/S0168-9274(98)00137-8","DOI":"10.1016\/S0168-9274(98)00137-8"},{"key":"10_CR15","doi-asserted-by":"publisher","unstructured":"Maroni, P.: New results about orthogonality preserving maps. J. Korean Math. Soc. 42(2), 243\u2013254 (2005). https:\/\/doi.org\/10.4134\/JKMS.2005.42.2.243","DOI":"10.4134\/JKMS.2005.42.2.243"},{"key":"10_CR16","doi-asserted-by":"publisher","unstructured":"Maroni, P., Mesquita, T.A.: Appell polynomial sequences with respect to some differential operators. Period. Math. Hungar. 72(2), 200\u2013217 (2016). https:\/\/doi.org\/10.1007\/s10998-016-0142-3","DOI":"10.1007\/s10998-016-0142-3"},{"key":"10_CR17","unstructured":"Mesquita, T.A.: About the (hahn) classical character of 2-orthogonal solutions of two families of differential equations of third order. arXiv: 2106.13046 (2021)"},{"key":"10_CR18","doi-asserted-by":"publisher","unstructured":"Mesquita, T.A.: Symbolic approach to 2-orthogonal polynomial solutions of a third order differential equation. Math. Comput. Sci. 16(1), 21 (2022). https:\/\/doi.org\/10.1007\/s11786-022-00525-8","DOI":"10.1007\/s11786-022-00525-8"},{"key":"10_CR19","doi-asserted-by":"publisher","unstructured":"Mesquita, T.A., Maroni, P.: Around operators not increasing the degree of polynomials. Integral Transforms Spec. Funct. 30(5), 383\u2013399 (2019). https:\/\/doi.org\/10.1080\/10652469.2019.1573423","DOI":"10.1080\/10652469.2019.1573423"},{"key":"10_CR20","doi-asserted-by":"publisher","unstructured":"Pincherle, S.: M\u00e9moire sur le calcul fonctionnel distributif. Math. Ann. 49, 325\u2013382 (1897). https:\/\/doi.org\/10.1007\/BF01444359","DOI":"10.1007\/BF01444359"},{"key":"10_CR21","doi-asserted-by":"publisher","unstructured":"Srivastava, H.M., Ben\u00a0Cheikh, Y.: Orthogonality of some polynomial sets via quasi-monomiality. Appl. Math. Comput. 141(2-3), 415\u2013425 (2003). https:\/\/doi.org\/10.1016\/S0096-3003(02)00961-X","DOI":"10.1016\/S0096-3003(02)00961-X"},{"key":"10_CR22","doi-asserted-by":"publisher","unstructured":"Van\u00a0Assche, W.: Nearest neighbor recurrence relations for multiple orthogonal polynomials. J. Approx. Theory 163(10), 1427\u20131448 (2011). https:\/\/doi.org\/10.1016\/j.jat.2011.05.003","DOI":"10.1016\/j.jat.2011.05.003"},{"key":"10_CR23","doi-asserted-by":"publisher","unstructured":"Van\u00a0Assche, W., Coussement, E.: Some classical multiple orthogonal polynomials. In: Gautschi, W., Marcell\u00e1n, F., Reichel, L. (eds.) Numerical Analysis 2000, Vol. V, Quadrature and Orthogonal Polynomials, vol. 127, pp. 317\u2013347. Elsevier (2001). https:\/\/doi.org\/10.1016\/S0377-0427(00)00503-3","DOI":"10.1016\/S0377-0427(00)00503-3"}],"container-title":["Coimbra Mathematical Texts","Orthogonal Polynomials and Special Functions"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-69646-6_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T20:07:36Z","timestamp":1735330056000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-69646-6_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031696459","9783031696466"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-69646-6_10","relation":{},"ISSN":["2813-0057","2813-0065"],"issn-type":[{"type":"print","value":"2813-0057"},{"type":"electronic","value":"2813-0065"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"28 December 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}