Gauss quadrature rules for the evaluation of $2\pi ^{-1/2} \int _0^\infty \exp (-x^2) f(x) dx$

Abstract:

Gauss quadrature rules for evaluating integrals of the form \[ 2{\pi ^{ - 1/2}} - \smallint _0^\infty \exp ( - {x^2})f(x)dx\] have been calculated to ${\text {20S}}$ for one to twenty nodes. The coefficients for the threeterm recurrence relation of the first twenty orthogonal polynomials associated with the weight function exp $( - {x^2})$ on the interval $[0, \infty )$ are also tabulated to $20{\text {S}}$.