Centrally symmetric orthogonal polynomials and second order partial differential equations

Abstract

We classify completely, up to a real change of variables, all differential equationswhich have centrally symmetric orthogonal polynomial solutions.

Tridiagonal Operators and Zeros of Polynomials in Two Variables

“…Furthermore, the properties of these polynomials or these operators are investigated. This is done, for example, in [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In other studies, as, for example, in [23], weight functions are constructed for certain orthogonal polynomials.…”

Two variable deformations of the Chebyshev measure

“…The general theory of bivariate orthogonal polynomials goes back to the work of Jackson [12]. Special examples have arisen in studies related to symmetric groups [4,16,22]), as extensions of one variable polynomials [7,15] and as eigenfunctions of partial differential equations [19,14,13,21]. An updated account of the theory can be found in the books [5,25].…”