Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic\nidentities satisfied by the zeros of a wide class of orthogonal polynomials is derived.The generalization is based on amodification of\npseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to\ndepend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family {
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