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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Article copyright:
© Copyright 1980
American Mathematical Society