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The computation of the entries of Jacobi operators associated with orthogonal polynomials on $\mathbb R$ has important applications in numerical analysis. From truncating the operator to form a Jacobi matrix, one can apply the Golub–Welsch algorithm (1969, Calculation of Gauss quadrature rules. Math. Comput., 23, 221) to compute the Gaussian quadrature weights and nodes. Furthermore, the entries o...

A Riemann–Hilbert approach to Jacobi operators and Gaussian quadrature