Gaussian quadratures for the integrals $_{0}^{\infty } \textrm {exp}(-x^{2})f(x)dx$ and $_{0}^{b} \textrm {exp}(-x^{2})f(x)dx$

Abstract:

Gaussian quadratures are developed for the evaluation of the integrals given in the title. The weights and abscissae for the semi-infinite integral are given for two through fifteen points with fifteen places. For $b = 1$, the weights and abscissae are given for two through ten points with fifteen places.