Pares coherentes generalizados de polinomios ortogonales en dos variables

En este trabajo nos centraremos en la obtención de pares x_k-coherentes de polinomios ortogonales en varias variables a partir de un sistema de polinomios ortogonales escogido inicialmente, concepto introducido en [28] de 2019 por Francisco Marcellán, Misael Marriaga, Teresa Pérez y Miguel Piñar, me...

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Autores:
Cortés Garzón, Juan Esteban
Tipo de recurso:
Fecha de publicación:
2023
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
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oai:repositorio.unal.edu.co:unal/84168
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/84168
https://repositorio.unal.edu.co/
Palabra clave:
510 - Matemáticas
Funciones ortogonales
Functions, orthogonal
Series, orthogonal
Series ortogonales
Polinomios Ortogonales
Varias Variables
Pares Coherentes
Programación
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_414d6b3e1cded725d49fc6e05155f2bc
oai_identifier_str oai:repositorio.unal.edu.co:unal/84168
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Pares coherentes generalizados de polinomios ortogonales en dos variables
dc.title.translated.eng.fl_str_mv Generalized Coherent Pairs of Orthogonal Polynomials in Two Variables
title Pares coherentes generalizados de polinomios ortogonales en dos variables
spellingShingle Pares coherentes generalizados de polinomios ortogonales en dos variables
510 - Matemáticas
Funciones ortogonales
Functions, orthogonal
Series, orthogonal
Series ortogonales
Polinomios Ortogonales
Varias Variables
Pares Coherentes
Programación
title_short Pares coherentes generalizados de polinomios ortogonales en dos variables
title_full Pares coherentes generalizados de polinomios ortogonales en dos variables
title_fullStr Pares coherentes generalizados de polinomios ortogonales en dos variables
title_full_unstemmed Pares coherentes generalizados de polinomios ortogonales en dos variables
title_sort Pares coherentes generalizados de polinomios ortogonales en dos variables
dc.creator.fl_str_mv Cortés Garzón, Juan Esteban
dc.contributor.advisor.none.fl_str_mv Pinzón Cortés, Natalia Camila
dc.contributor.author.none.fl_str_mv Cortés Garzón, Juan Esteban
dc.subject.ddc.spa.fl_str_mv 510 - Matemáticas
topic 510 - Matemáticas
Funciones ortogonales
Functions, orthogonal
Series, orthogonal
Series ortogonales
Polinomios Ortogonales
Varias Variables
Pares Coherentes
Programación
dc.subject.lemb.spa.fl_str_mv Funciones ortogonales
dc.subject.lemb.eng.fl_str_mv Functions, orthogonal
Series, orthogonal
dc.subject.lemb.spe.fl_str_mv Series ortogonales
dc.subject.proposal.spa.fl_str_mv Polinomios Ortogonales
Varias Variables
Pares Coherentes
Programación
description En este trabajo nos centraremos en la obtención de pares x_k-coherentes de polinomios ortogonales en varias variables a partir de un sistema de polinomios ortogonales escogido inicialmente, concepto introducido en [28] de 2019 por Francisco Marcellán, Misael Marriaga, Teresa Pérez y Miguel Piñar, mediante el uso de programación en el software Wolfram Mathematica. (Texto tomado de la fuente)
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-07-07T20:15:55Z
dc.date.available.none.fl_str_mv 2023-07-07T20:15:55Z
dc.date.issued.none.fl_str_mv 2023-06
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/84168
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/84168
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.references.spa.fl_str_mv Álvarez-Nodarse, Renato: Monogr. Semin. Mat. García Galdeano. Vol. 26: Polinomios hipergeométricos clásicos y q-polinomios. Zaragoza: Prensas Universitarias de Zaragoza, 2003. – ISBN 84–7733–637–7.
Appell, P. ; Kampé de Fériet, J.: Fonctions hypergéométriques et hypersphériques. Polynômes d’Hermite. 1926.
Area, Iván: Hypergeometric multivariate orthogonal polynomials. En: Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5–12, 2018. Cham: Birkhäuser, 2020. – ISBN 978–3–030–36743–5; 978–3–030–36746–6; 978–3–030– 36744–2, p. 165–193.
Area, Iván. ; Godoy, E. ; Ronveaux, A. ; Zarzo, A.: Bivariate second-order linear partial differential equations and orthogonal polynomial solutions. En: J. Math. Anal.Appl. 387 (2012), Nr. 2, p. 1188–1208. – ISSN 0022–247X.
Barrio, Roberto ; Peña, Juan M. ; Sauer, Tomas: Three term recurrence for the evaluation of multivariate orthogonal polynomials. En: Journal of Approximation Theory 162 (2010), Nr. 2, p. 407–420. – ISSN 0021–9045.
Chihara, T.S.: An Introduction to Orthogonal Polynomials. Gordon and Breach, 1978.
Delgado, Antonia M.: Ortogonalidad no estándar: Problemas Directos e Inversos, Doctoral Dissertation, Universidad Carlos III de Madrid. In Spanish, Tesis de Grado, 2006.
Delgado, Antonia M. ; Geronimo, Jeffrey S. ; Iliev, Plamen ; Marcellán, Francisco: Two variable orthogonal polynomials and structured matrices. En: SIAM J. Matrix Anal. Appl. 28 (2006), Nr. 1, p. 118–147. – ISSN 0895–4798.
Delgado, Antonia M. ; Marcellán, Francisco: Companion linear functionals and Sobolev inner products: a case study. En: Methods Appl. Anal. 11 (2004), Nr. 2, p. 237–266.
Delgado, Antonia M. ; Marcellán, Francisco: On an extension of symmetric coherent pairs of orthogonal polynomials. En: J. Comput. Appl. Math. 178 (2005), Nr. 1-2, p. 155–168.
Dunkl, Charles F. ; Xu, Yuan: Orthogonal polynomials of several variables. Cambridge: Cambridge University Press, 2001 (Encycl. Math. Appl.). ISSN 0953–4806.
Engelis, G. K.: On some two-dimensional analogues of the classical orthogonal polynomials. En: Latv. Mat. Ezheg. 15 (1974), p. 169–202. – ISSN 0321–2270.
Fernández, Lidia ; Pérez, Teresa E. ; Piñar, Miguel A.: Classical orthogonal polynomials in two variables: a matrix approach. En: Numer. Algorithms 39 (2005), Nr. 1-3, p. 131–142. – ISSN 1017–1398.
Garza, Luis ; Marcellán, Francisco ; Pinzón-Cortés, Natalia C.: (1, 1)-coherent pairs on the unit circle. En: Abstr. Appl. Anal. 2013 (2013), p. 8. – Id/No 307974. – ISSN 1085–3375.
Hahn, Wolfgang: Über die Jacobischen Polynome und zwei verwandte Polynomklassen. En: Mathematische Zeitschrift 39 (1935), p. 634–638.
Hermite, M. ; des sciences (France), Académie: Sur Un Nouveau Développement en Série Des Fonctions. Imprimerie de Gauthier-Villars, 1864.
Iserles, Arieh ; Koch, P. E. ; Nørsett, Syvert P. ; Sanz-Serna, J. M.: On polynomials orthogonal with respect to certain Sobolev inner products. En: J. Approx. Theory 65 (1991), Nr. 2, p. 151–175. – ISSN 0021–9045.
Jacobi, C.G.J.: Untersuchungen über die Differentialgleichung der hypergeometrischen Reihe. 1859 (1859), Nr. 56, p. 149–165.
de Jesus, M. N. ; Marcellán, Francisco. ; Petronilho, J. ; Pinzón-Cortés, N. C.: (M,N)-coherent pairs of order (m, n) and Sobolev orthogonal polynomials. En: J. Comput. Appl. Math. 256 (2014), p. 16–35. – ISSN 0377–0427.
Karlin, S. ; McGregor, J. On some stochastic models in genetics. Stochastic Models Med. Biol., Proc. Sympos. Univ. Wisconsin 1963, 245-279. 1964.
Karlin, S. ; McGregor, J.: Linear Growth Models with Many Types and Multidimensional Hahn Polynomials. En: Askey, Richard A. (Ed.): Theory and Application of Special Functions. Academic Press, 1975. – ISBN 978–0–12–064850–4, p. 261–288.
Koornwinder, Tom: Two-Variable Analogues of the Classical Orthogonal Polynomials. En: Askey, Richard A. (Ed.): Theory and Application of Special Functions. Academic Press, 1975. – ISBN 978–0–12–064850–4, p. 435–495.
Kowalski, M. A.: Orthogonality and recursion formulas for polynomials in n variables. En: SIAM J. Math. Anal. 13 (1982), p. 316–323. – ISSN 0036–1410.
Kowalski, M. A.: The recursion formulas for orthogonal polynomials in n variables. En: SIAM J. Math. Anal. 13 (1982), p. 309–315. – ISSN 0036–1410.
Krall, H. L. ; Frink, Orrin: A new class of orthogonal polynomials: The Bessel polynomials. En: Trans. Am. Math. Soc. 65 (1949), p. 100–115. – ISSN 0002–9947.
Krall, H. L. ; Sheffer, I. M.: Orthogonal polynomials in two variables. En: Ann. Mat. Pura Appl. (4) 76 (1967), p. 325–376. – ISSN 0373–3114.
Legendre, Adrien M.: Recherches sur l’attraction des spheroides homogenes. En: Mémoires de mathématique et de physique : prés. á l’Acad´emie Royale des Sciences, par divers savans, et lûs dans ses assemblées 1785 (2007), p. 411 – 434.
Marcellán, Francisco ; Marriaga, Misael E. ; Pérez, Teresa E. ; Piñar, Miguel A.: Coherent pairs of bivariate orthogonal polynomials. En: J. Approx. Theory 245 (2019), p. 40–63. – ISSN 0021–9045.
Marcellán, Francisco ; Pérez, Teresa E. ; Piñar, Miguel A.: Orthogonal polynomials on weighted Sobolev spaces: The semiclassical case. En: Ann. Numer. Math. 2 (1995), Nr. 1-4, p. 93–122. – ISSN 1021–2655.
Marcellán, Francisco ; Petronilho, J.: Orthogonal polynomials and coherent pairs: The classical case. En: Indag. Math., New Ser. 6 (1995), Nr. 3, p. 287–307. – ISSN 0019–3577.
Marcellán, Francisco ; Petronilho, José C. ; Pérez, Teresa E. ; Piñar, Miguel A.: What is beyond coherent pairs of orthogonal polynomials? En: J. Comput. Appl. Math. 65 (1995), Nr. 1-3, p. 267–277. – ISSN 0377–0427.
Marcellán, Francisco ; Pinzón-Cortés, Natalia C.: (1, 1)-q-coherent pairs. En: Numer. Algorithms 60 (2012), Nr. 2, p. 223–239. – ISSN 1017–1398.
Marcellán, Francisco ; Pinzón-Cortés, Natalia C.: (1, 1)-Dω-coherent pairs. En: J. Difference Equ. Appl. 19 (2013), Nr. 11, p. 1828–1848. – ISSN 1023–6198.
Meijer, H. G.: Coherent pairs and zeros of Sobolev-type orthogonal polynomials. En: Indag. Math., New Ser. 4 (1993), Nr. 2, p. 163–176. – ISSN 0019–3577.
Meijer, H. G.: Determination of all coherent pairs. En: J. Approx. Theory 89 (1997), Nr. 3, p. 321–343. – ISSN 0021–9045.
Proriol, Joseph: Sur une famille de polynômes à deux variables orthogonaux dans un triangle. En: C. R. Acad. Sci., Paris 245 (1957), p. 2459–2461. – ISSN 0001–4036.
Stieltjes, T.-J.: Recherches sur les fractions continues. En: Annales de la Faculté des sciences de Toulouse : Mathématiques 8 (1894), Nr. 4, p. J1–J122.
Suetin, P. K.: Anal. Methods Spec. Funct.. Vol. 3: Orthogonal polynomials in two variables. Transl. from the 1988 Russian original by E. V. Pankratiev . Amsterdam: Gordon and Breach Science Publishers, 1999. – ISBN 90–5699–167–1.
Szegö, Gábor: Colloq. Publ., Am. Math. Soc.. Vol. 23: Orthogonal polynomials. American Mathematical Society (AMS), Providence, RI, 1939 ISSN 0065–9258.
Tchebychev, Pafnutii L.: Théorie des mécanismes connus sous le nom de parallélogrammes. Imprimerie de l’Académie impériale des sciences, 1853.
Tchebyshev, Pafnutii L.: Sur le développement des fonctions à une seule variable. En: Bull. Acad. Sci. St. Petersb 1 (1859), Nr. 193-200, p. 124.
Wolfram Research, Inc. Mathematica, Version 12.1. Champaign, Illinois, (2020).
Zernike, F. ; Brinkman, H. C.: Hypersphärische Funktionen und die in sphärischen Bereichen orthogonalen Polynome. En: Proc. Akad. Wet. Amsterdam 38 (1935), p. 161–170. – ISSN 0370–0348.
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dc.format.extent.spa.fl_str_mv vii, 46 páginas
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dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv Bogotá - Ciencias - Maestría en Ciencias - Matemáticas
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv Bogotá,Colombia
dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá
institution Universidad Nacional de Colombia
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spelling Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Pinzón Cortés, Natalia Camila4a612934f85871565b47483201ed4e44Cortés Garzón, Juan Estebane239e2a6e623e40849eeeae7c0cc37f62023-07-07T20:15:55Z2023-07-07T20:15:55Z2023-06https://repositorio.unal.edu.co/handle/unal/84168Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/En este trabajo nos centraremos en la obtención de pares x_k-coherentes de polinomios ortogonales en varias variables a partir de un sistema de polinomios ortogonales escogido inicialmente, concepto introducido en [28] de 2019 por Francisco Marcellán, Misael Marriaga, Teresa Pérez y Miguel Piñar, mediante el uso de programación en el software Wolfram Mathematica. (Texto tomado de la fuente)In this work we will focus on obtaining xk-coherent pairs of orthogonal polynomials in several variables from an initially chosen system of orthogonal polynomials, a concept introduced in [28] of 2019 by Francisco Marcellán, Misael Marriaga, Teresa Pérez and Miguel Piñar, by using programming in Wolfram Mathematica software.MaestríaMagíster en Ciencias - Matemáticasvii, 46 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá,ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - MatemáticasFunciones ortogonalesFunctions, orthogonalSeries, orthogonalSeries ortogonalesPolinomios OrtogonalesVarias VariablesPares CoherentesProgramaciónPares coherentes generalizados de polinomios ortogonales en dos variablesGeneralized Coherent Pairs of Orthogonal Polynomials in Two VariablesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMÁlvarez-Nodarse, Renato: Monogr. Semin. Mat. García Galdeano. Vol. 26: Polinomios hipergeométricos clásicos y q-polinomios. Zaragoza: Prensas Universitarias de Zaragoza, 2003. – ISBN 84–7733–637–7.Appell, P. ; Kampé de Fériet, J.: Fonctions hypergéométriques et hypersphériques. Polynômes d’Hermite. 1926.Area, Iván: Hypergeometric multivariate orthogonal polynomials. En: Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5–12, 2018. Cham: Birkhäuser, 2020. – ISBN 978–3–030–36743–5; 978–3–030–36746–6; 978–3–030– 36744–2, p. 165–193.Area, Iván. ; Godoy, E. ; Ronveaux, A. ; Zarzo, A.: Bivariate second-order linear partial differential equations and orthogonal polynomial solutions. En: J. Math. Anal.Appl. 387 (2012), Nr. 2, p. 1188–1208. – ISSN 0022–247X.Barrio, Roberto ; Peña, Juan M. ; Sauer, Tomas: Three term recurrence for the evaluation of multivariate orthogonal polynomials. En: Journal of Approximation Theory 162 (2010), Nr. 2, p. 407–420. – ISSN 0021–9045.Chihara, T.S.: An Introduction to Orthogonal Polynomials. Gordon and Breach, 1978.Delgado, Antonia M.: Ortogonalidad no estándar: Problemas Directos e Inversos, Doctoral Dissertation, Universidad Carlos III de Madrid. In Spanish, Tesis de Grado, 2006.Delgado, Antonia M. ; Geronimo, Jeffrey S. ; Iliev, Plamen ; Marcellán, Francisco: Two variable orthogonal polynomials and structured matrices. En: SIAM J. Matrix Anal. Appl. 28 (2006), Nr. 1, p. 118–147. – ISSN 0895–4798.Delgado, Antonia M. ; Marcellán, Francisco: Companion linear functionals and Sobolev inner products: a case study. En: Methods Appl. Anal. 11 (2004), Nr. 2, p. 237–266.Delgado, Antonia M. ; Marcellán, Francisco: On an extension of symmetric coherent pairs of orthogonal polynomials. En: J. Comput. Appl. Math. 178 (2005), Nr. 1-2, p. 155–168.Dunkl, Charles F. ; Xu, Yuan: Orthogonal polynomials of several variables. Cambridge: Cambridge University Press, 2001 (Encycl. Math. Appl.). ISSN 0953–4806.Engelis, G. K.: On some two-dimensional analogues of the classical orthogonal polynomials. En: Latv. Mat. Ezheg. 15 (1974), p. 169–202. – ISSN 0321–2270.Fernández, Lidia ; Pérez, Teresa E. ; Piñar, Miguel A.: Classical orthogonal polynomials in two variables: a matrix approach. En: Numer. Algorithms 39 (2005), Nr. 1-3, p. 131–142. – ISSN 1017–1398.Garza, Luis ; Marcellán, Francisco ; Pinzón-Cortés, Natalia C.: (1, 1)-coherent pairs on the unit circle. En: Abstr. Appl. Anal. 2013 (2013), p. 8. – Id/No 307974. – ISSN 1085–3375.Hahn, Wolfgang: Über die Jacobischen Polynome und zwei verwandte Polynomklassen. En: Mathematische Zeitschrift 39 (1935), p. 634–638.Hermite, M. ; des sciences (France), Académie: Sur Un Nouveau Développement en Série Des Fonctions. Imprimerie de Gauthier-Villars, 1864.Iserles, Arieh ; Koch, P. E. ; Nørsett, Syvert P. ; Sanz-Serna, J. M.: On polynomials orthogonal with respect to certain Sobolev inner products. En: J. Approx. Theory 65 (1991), Nr. 2, p. 151–175. – ISSN 0021–9045.Jacobi, C.G.J.: Untersuchungen über die Differentialgleichung der hypergeometrischen Reihe. 1859 (1859), Nr. 56, p. 149–165.de Jesus, M. N. ; Marcellán, Francisco. ; Petronilho, J. ; Pinzón-Cortés, N. C.: (M,N)-coherent pairs of order (m, n) and Sobolev orthogonal polynomials. En: J. Comput. Appl. Math. 256 (2014), p. 16–35. – ISSN 0377–0427.Karlin, S. ; McGregor, J. On some stochastic models in genetics. Stochastic Models Med. Biol., Proc. Sympos. Univ. Wisconsin 1963, 245-279. 1964.Karlin, S. ; McGregor, J.: Linear Growth Models with Many Types and Multidimensional Hahn Polynomials. En: Askey, Richard A. (Ed.): Theory and Application of Special Functions. Academic Press, 1975. – ISBN 978–0–12–064850–4, p. 261–288.Koornwinder, Tom: Two-Variable Analogues of the Classical Orthogonal Polynomials. En: Askey, Richard A. (Ed.): Theory and Application of Special Functions. Academic Press, 1975. – ISBN 978–0–12–064850–4, p. 435–495.Kowalski, M. A.: Orthogonality and recursion formulas for polynomials in n variables. En: SIAM J. Math. Anal. 13 (1982), p. 316–323. – ISSN 0036–1410.Kowalski, M. A.: The recursion formulas for orthogonal polynomials in n variables. En: SIAM J. Math. Anal. 13 (1982), p. 309–315. – ISSN 0036–1410.Krall, H. L. ; Frink, Orrin: A new class of orthogonal polynomials: The Bessel polynomials. En: Trans. Am. Math. Soc. 65 (1949), p. 100–115. – ISSN 0002–9947.Krall, H. L. ; Sheffer, I. M.: Orthogonal polynomials in two variables. En: Ann. Mat. Pura Appl. (4) 76 (1967), p. 325–376. – ISSN 0373–3114.Legendre, Adrien M.: Recherches sur l’attraction des spheroides homogenes. En: Mémoires de mathématique et de physique : prés. á l’Acad´emie Royale des Sciences, par divers savans, et lûs dans ses assemblées 1785 (2007), p. 411 – 434.Marcellán, Francisco ; Marriaga, Misael E. ; Pérez, Teresa E. ; Piñar, Miguel A.: Coherent pairs of bivariate orthogonal polynomials. En: J. Approx. Theory 245 (2019), p. 40–63. – ISSN 0021–9045.Marcellán, Francisco ; Pérez, Teresa E. ; Piñar, Miguel A.: Orthogonal polynomials on weighted Sobolev spaces: The semiclassical case. En: Ann. Numer. Math. 2 (1995), Nr. 1-4, p. 93–122. – ISSN 1021–2655.Marcellán, Francisco ; Petronilho, J.: Orthogonal polynomials and coherent pairs: The classical case. En: Indag. Math., New Ser. 6 (1995), Nr. 3, p. 287–307. – ISSN 0019–3577.Marcellán, Francisco ; Petronilho, José C. ; Pérez, Teresa E. ; Piñar, Miguel A.: What is beyond coherent pairs of orthogonal polynomials? En: J. Comput. Appl. Math. 65 (1995), Nr. 1-3, p. 267–277. – ISSN 0377–0427.Marcellán, Francisco ; Pinzón-Cortés, Natalia C.: (1, 1)-q-coherent pairs. En: Numer. Algorithms 60 (2012), Nr. 2, p. 223–239. – ISSN 1017–1398.Marcellán, Francisco ; Pinzón-Cortés, Natalia C.: (1, 1)-Dω-coherent pairs. En: J. Difference Equ. Appl. 19 (2013), Nr. 11, p. 1828–1848. – ISSN 1023–6198.Meijer, H. G.: Coherent pairs and zeros of Sobolev-type orthogonal polynomials. En: Indag. Math., New Ser. 4 (1993), Nr. 2, p. 163–176. – ISSN 0019–3577.Meijer, H. G.: Determination of all coherent pairs. En: J. Approx. Theory 89 (1997), Nr. 3, p. 321–343. – ISSN 0021–9045.Proriol, Joseph: Sur une famille de polynômes à deux variables orthogonaux dans un triangle. En: C. R. Acad. Sci., Paris 245 (1957), p. 2459–2461. – ISSN 0001–4036.Stieltjes, T.-J.: Recherches sur les fractions continues. En: Annales de la Faculté des sciences de Toulouse : Mathématiques 8 (1894), Nr. 4, p. J1–J122.Suetin, P. K.: Anal. Methods Spec. Funct.. Vol. 3: Orthogonal polynomials in two variables. Transl. from the 1988 Russian original by E. V. Pankratiev . Amsterdam: Gordon and Breach Science Publishers, 1999. – ISBN 90–5699–167–1.Szegö, Gábor: Colloq. Publ., Am. Math. Soc.. Vol. 23: Orthogonal polynomials. American Mathematical Society (AMS), Providence, RI, 1939 ISSN 0065–9258.Tchebychev, Pafnutii L.: Théorie des mécanismes connus sous le nom de parallélogrammes. Imprimerie de l’Académie impériale des sciences, 1853.Tchebyshev, Pafnutii L.: Sur le développement des fonctions à une seule variable. En: Bull. Acad. Sci. St. Petersb 1 (1859), Nr. 193-200, p. 124.Wolfram Research, Inc. Mathematica, Version 12.1. Champaign, Illinois, (2020).Zernike, F. ; Brinkman, H. C.: Hypersphärische Funktionen und die in sphärischen Bereichen orthogonalen Polynome. En: Proc. Akad. Wet. 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