Second Order Difference Equations and Discrete Orthogonal Polynomials of Two Variables
نویسنده
چکیده
The second order partial difference equation of two variables Du := A1,1(x)∆1∇1u+A1,2(x)∆1∇2u+ A2,1(x)∆2∇1u+ A2,2(x)∆2∇2u + B1(x)∆1u+ B2(x)∆2u = λu, is studied to determine when it has orthogonal polynomials as solutions. We derive conditions on D so that a weight function W exists for which WDu is self-adjoint and the difference equation has polynomial solutions which are orthogonal with respect to W . The solutions are essentially the classical discrete orthogonal polynomials of two variables.
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