Results on the Colombeau Products of the Distribution $x_+^{-r-1/2}$ with the Distributions $x_-^{-k-1/2}$ and $x_-^{k-1/2}$

Results on the products of the distribution $x_+^{-r-1/2}$ with the distributions $x_-^{-k-1/2}$ and $x_-^{k-1/2}$ are obtained in the differential algebra ${\mathcal{G}}(\mathbb{R})$ of Colombeau generalized functions, which contains the space $\mathcal{D}'(\mathbb{R})$ of Schwartz distributions as a subspace; in this algebra the notion of association is defined, which is a faithful generalization of weak equality in $\mathcal{G}(\mathbb{R})$. This enables treating the results in terms of distributions again.