A Necessary and Sufficient Condition for Nonnegative Product Linearization of Orthogonal Polynomials
نویسندگان
چکیده
cos nθ cos mθ = 2 cos(n − m)θ + 2 cos(n + m)θ. Certain classical orthogonal polynomials admit explicit computation of the coefficients c(n,m, k). For example, they are known explicitly for the ultraspherical polynomials along with their q-analogs [8]. However, they are not available in a simple form for the nonsymmetric Jacobi polynomials (see [7]). The first general criterion for nonnegativity of linearization coefficients is due to Askey [1]. Although it is pretty strong it is not strong enough to cover all classes of the ultraspherical polynomials. It is well-known that the problem of product linearization is equivalent to a certain discrete hyperbolic boundary value problem. This approach has been used in [6], [9] to derive new criteria for nonnegative linearization. The new criteria
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