ORTHOGONAL POLYNOMIALS SATISFYING PARTIAL DIFFERENTIAL EQUATIONS BELONGING TO THE BASIC CLASS

Title & Authors
ORTHOGONAL POLYNOMIALS SATISFYING PARTIAL DIFFERENTIAL EQUATIONS BELONGING TO THE BASIC CLASS
Lee, J.K.; L.L. Littlejohn; Yoo, B.H.;

Abstract
We classify all partial differential equations with polynomial coefficients in $\small{\chi}$ and y of the form A($\small{\chi}$) $\small{u_{{\chi}{\chi}}}$ ＋ 2B($\small{\chi}$, y) $\small{u_{{\chi}y}}$ ＋ C(y) $\small{u_{yy}}$ ＋ D($\small{\chi}$) $\small{u_{{\chi}}}$ ＋ E(y) $\small{u_{y}}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.
Keywords
orthogonal polynomials in two variables;partial differential equation in the basic class;
Language
English
Cited by
1.
Bivariate orthogonal polynomials in the Lyskova class, Journal of Computational and Applied Mathematics, 2009, 233, 3, 597
2.
Sobolev orthogonal polynomials in two variables and second order partial differential equations, Journal of Mathematical Analysis and Applications, 2006, 322, 2, 1001
3.
Tridiagonal Operators and Zeros of Polynomials in Two Variables, Abstract and Applied Analysis, 2016, 2016, 1
4.
On differential properties for bivariate orthogonal polynomials, Numerical Algorithms, 2007, 45, 1-4, 153
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