Orthogonal Polynomials Satisfying Partial Differential Equations Belonging to the Basic Class
نویسندگان
چکیده
We classify all partial di¤erential equations with polynomial coe¢ cients in x and y of the form A(x)uxx + 2B(x; y)uxy + C(y)uyy +D(x)ux + E(y)uy = nu; which has weak orthogonal polynomials as solutions and show that partial derivatives of all order are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial di¤erential equations in d-variables.
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