Bivariate orthogonal polynomials in the Lyskova class

• Published in: Journal of computational and applied mathematics Vol. 233; no. 3; pp. 597 - 601
• Main Authors: ALVAREZ DE MORALES, María, FERNANDEZ, Lidia, PEREZ, Teresa E, PINAR, Miguel A
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 01.12.2009; Elsevier
• Subjects: Algebra; Classical orthogonal polynomials in two variables; Exact sciences and technology; Fourier analysis; Linear and multilinear algebra, matrix theory; Lyskova class; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Special functions; 33C50; Lyskova class; Classical orthogonal polynomials in two variables; 42C05; Second order equation; variables; Differential equation; Initial value problem; Polynomial equation; Partial differential equation; Orthogonal polynomial; Numerical analysis; Boundary value problem; Applied mathematics; Classical orthogonal polynomials in two; Matrix equation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2009.02.027

Classical orthogonal polynomials in two variables can be characterized as the polynomial solutions of a matrix second-order partial differential equation involving matrix polynomial coefficients. In this work, we study classical orthogonal polynomials in two variables whose partial derivatives satisfy again a second-order partial differential equation of the same type.