given explicitly in the appendix, forms the basis for the numerical investigation undertaken here. The approach used in evaluating these equations is to express each [*element*]{} of the matrices(vectors) in the five-component space of coefficient functions as a [*matrix*]{}([*vector*]{}) in the direct-product space of the magnitude of the momentum $P$ and the direction cosine $C_{Pq}$. The value of the photon momentum, $q^2$, is a parameter of the equations. That is, for each value of $q^2$ a different set of equations is obtained. For the numerical evaluation, the momentum $P$ and the direction cosine $C_{Pq}$ are discretized in terms of Gauss-quadrature points. The integrations are then carried out as matrix multiplication. The coupled equations are solved as a matrix equation in the expanded direct-product space of the coefficient functions and the Gauss integration points. The dimension of the equation is given by 5$\times $nppts$\times $ncpts, where nppts and ncpts are the number of Gauss points representing the $P$ and $C_{Pq}$ integrations respectively. The number of points in both integrations is varied to ensure accuracy. For the momentum, twenty to forty quadrature points are used, while six to ten are used for the direction cosine.

### Gluon two-point function ansatz

The aim 