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In this contribution, we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function \(w(x)= x^{\alpha } \mathrm{e} ^{-x}\) , \(\alpha > -1\) , supported on an interval \((0,z)\) , \(z>0\) . The modified Chebyshev algorithm is used in order to test the accuracy in the computation of the coefficients of the three-term recurrence relation, the zeros, and weights as well as the dependence on the parameter z.

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A Note on Laguerre Truncated Polynomials and Quadrature Formula

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  • 发表日期：

    2025年

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  • Juan C. García-Ardila,
  • Francisco Marcellán

摘要

In this contribution, we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function \(w(x)= x^{\alpha } \mathrm{e} ^{-x}\) , \(\alpha > -1\) , supported on an interval \((0,z)\) , \(z>0\) . The modified Chebyshev algorithm is used in order to test the accuracy in the computation of the coefficients of the three-term recurrence relation, the zeros, and weights as well as the dependence on the parameter z.