A Note on Laguerre Truncated Polynomials and Quadrature Formula

Juan C. García-Ardila () and Francisco Marcellán ()
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Juan C. García-Ardila: Universidad Politécnica de Madrid
Francisco Marcellán: Universidad Carlos III de Madrid

Chapter Chapter 8 in Analysis, Approximation, Optimization: Computation and Applications, 2025, pp 135-154 from Springer

Abstract: Abstract In this contribution, we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function w ( x ) = x α e − x $$w(x)= x^{\alpha } \mathrm{e} ^{-x}$$ , α > −1 $$\alpha > -1$$ , supported on an interval ( 0 , z ) $$(0,z)$$ , z > 0 $$z>0$$ . 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.

Date: 2025
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DOI: 10.1007/978-3-031-85743-0_8

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