Abstract
We construct the linear differential equations of third order satisfied by the classical
We construct the linear differential equations of third order satisfied by the classical
A. I. Aptekarev, “Multiple orthogonal polynomials,” Journal of Computational and Applied Mathematics, vol. 99, no. 1-2, pp. 423–447, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. I. Aptekarev, A. Branquinho, and W. Van Assche, “Multiple orthogonal polynomials for classical weights,” Transactions of the American Mathematical Society, vol. 355, no. 10, pp. 3887–3914, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. I. Aptekarev, F. Marcellán, and I. A. Rocha, “Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials,” Journal of Approximation Theory, vol. 90, no. 1, pp. 117–146, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Arvesú, J. Coussement, and W. Van Assche, “Some discrete multiple orthogonal polynomials,” Journal of Computational and Applied Mathematics, vol. 153, no. 1-2, pp. 19–45, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Bochner, “Über Sturm-Liouvillesche Polynomsysteme,” Mathematische Zeitschrift, vol. 29, no. 1, pp. 730–736, 1929.
View at: Publisher Site | Google Scholar | MathSciNetA. Boukhemis, “A study of a sequence of classical orthogonal polynomials of dimension ,” Journal of Approximation Theory, vol. 90, no. 3, pp. 435–454, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. Boukhemis, “On the classical 2-orthogonal polynomials sequences of Sheffer-Meixner type,” Cubo. A Mathematical Journal, vol. 7, no. 2, pp. 39–55, 2005.
View at: Google Scholar | MathSciNetA. Boukhemis and P. Maroni, “Une caractérisation des polynômes strictement orthogonaux de type Scheffer. Étude du cas ,” Journal of Approximation Theory, vol. 54, no. 1, pp. 67–91, 1988.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Douak and P. Maroni, “Les polynômes orthogonaux “classiques” de dimension deux,” Analysis, vol. 12, no. 1-2, pp. 71–107, 1992.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Douak and P. Maroni, “On -orthogonal Tchebychev polynomials. I,” Applied Numerical Mathematics, vol. 24, no. 1, pp. 23–53, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Douak and P. Maroni, “On -orthogonal Tchebychev polynomials. II,” Methods and Applications of Analysis, vol. 4, no. 4, pp. 404–429, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Favard, “Sur les polynômes de Tchebicheff,” Comptes Rendus de l'Académie des Sciences, Paris, vol. 200, pp. 2052–2053, 1935.
View at: Google Scholar | Zentralblatt MATHW. Hahn, “Über die Jacobischen Polynome und zwei verwandte Polynomklassen,” Mathematische Zeitschrift, vol. 39, no. 1, pp. 634–638, 1935.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. V. Ho, J. W. Jayne, and M. B. Sledd, “Recursively generated Sturm-Liouville polynomial systems,” Duke Mathematical Journal, vol. 33, no. 1, pp. 131–140, 1966.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. L. Krall, “On derivatives of orthogonal polynomials I,” Bulletin of the American Mathematical Society, vol. 42, pp. 423–428, 1936.
View at: Google Scholar | Zentralblatt MATHP. Maroni, “L'orthogonalité et les récurrences de polynômes d'ordre supérieur à deux,” Toulouse. Faculté des Sciences. Annales. Mathématiques. Série 5, vol. 10, no. 1, pp. 105–139, 1989.
View at: Google Scholar | Zentralblatt MATH | MathSciNetE. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality, vol. 92 of Translations of Mathematical Monographs, American Mathematical Society, Rhode Island, 1991.
View at: Zentralblatt MATH | MathSciNetJ. Shohat, “Sur les polynômes orthogonaux généralisés,” Comptes Rendus de l'Académie des Sciences, Paris, vol. 207, pp. 556–558, 1938.
View at: Google Scholar | Zentralblatt MATHW. Van Assche, “Multiple orthogonal polynomials, irrationality and transcendence,” in Continued Fractions: From Analytic Number Theory to Constructive Approximation (Columbia, MO, 1998), B. C. Berndt and F. Gesztezy, Eds., vol. 236 of Contemporary Mathematics, pp. 325–342, American Mathematical Society, Rhode Island, 1999.
View at: Google Scholar | MathSciNetW. Van Assche and E. Coussement, “Some classical multiple orthogonal polynomials,” Journal of Computational and Applied Mathematics, vol. 127, no. 1-2, pp. 317–347, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Van Iseghem, Approximants de Padé vectoriels, Thèse d'Etat, l'Université des Sciences et Techniques de Lille-Flandre-Artois, Lille, 1987.