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Mathematics of Computation

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Gaussian quadrature of integrands involving the error function


Authors: J. P. Vigneron and Ph. Lambin
Journal: Math. Comp. 35 (1980), 1299-1307
MSC: Primary 65A05; Secondary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1980-0583507-1
MathSciNet review: 583507
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Abstract: Orthogonal polynomials corresponding to the weight function $ 1 - {\operatorname{erf}}(x)$ and defined on the positive real axis are constructed. Abscissas and weight factors for the associated Gaussian quadrature are then deduced (up to 12-point formulas). The stability of the algorithm used for this particular computation is discussed. An example is provided to test the efficiency of the new Gaussian rule.


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DOI: https://doi.org/10.1090/S0025-5718-1980-0583507-1
Article copyright: © Copyright 1980 American Mathematical Society