The set of Associated Homogeneous Distributions (AHDs) on R, H(R), consists of distributional analogues of power-log functions with domain in R. This set contains the majority of the (one-dimensional) distributions typically encountered in physics applications. In earlier work of the author it was shown that H(R) admits a closed convolution structure, provided that critical convolution products are defined by a functional extension process. In this paper, the general convolution product formula is derived. Convolution of AHDs on R is found to be associative, except for critical triple products. Critical products are shown to be non-associative in a minimal and interesting way.