ABSTRACT
An expert on numerical integration techniques would undoubtedly object to the author's neglect of the various forms of Gaussian integration, and the author has not attempted to give a full view of all possible methods. A change of the variable of integration is often tried in analytic integration, and an example of its use in numerical integration was given earlier. There are several other cases of relevance in physics where such a procedure is useful. The exp factor, giving so-called Gaussian orbitals, is favoured in some parts of quantum chemistry, particularly where multi-centre integrals are involved, since a product of Gaussian functions on two different origins can be expressed in terms of Gaussians centred on some third point. However, in simple atomic problems it has been found that many Gaussian orbitals are needed to represent a typical atomic orbital functions with exp factors give a more compact basis set for atomic problems.
