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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
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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Article copyright: © Copyright 1980 American Mathematical Society