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Gaussian quadrature; orthogonal polynomials; Kronrod extensions; Patterson sequences; imbedded quadratures; Laguerre weight function; Hermite weight function; quadrature formulae; maximal polynomial order of precision
We present algorithms for the determination of polynomials orthogonal with respect to a positive weight function multiplied by a polynomial with simple roots inside the interval of integration. We apply these algorithms to search for and calculate all possible sequences of imbedded quadratures of maximal polynomials order of precision for the generalized Laguerre and Hermite weight functions.
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