ORTHOGONAL POLYNOMIALS SATISFYING PARTIAL DIFFERENTIAL EQUATIONS BELONGING TO THE BASIC CLASS Lee, J.K.; L.L. Littlejohn; Yoo, B.H.;
We classify all partial differential equations with polynomial coefficients in and y of the form A() ＋ 2B(, y) ＋ C(y) ＋ D() ＋ E(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.
orthogonal polynomials in two variables;partial differential equation in the basic class;