Gaussian quadrature of integrands involving the error function
J.-P. Vigneron, Ph. Lambin · Mathematics of Computation · 1980
Orthogonal polynomials corresponding to the weight function 1 − erf ( x ) 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.