On the Evaluation of Correction Terms of Gaussian Integration

Accurate and compact computing recipe for evaluating correction terms for the Gaussian integration of analytic functions offers economy and high accuracy for many integrals of interest in physical sciences. The requirement of numerical integration in physical sciences is quite pervasive because many practical functions aren't integrable in closed form. A simple example is the error function Erβx) defined by1 Erf(x) 2 /<; dt.