On the incomplete gamma function and its neutrix convolution for negative integers

We define the distributions $\gamma^+(-r,x)$ and $\gamma^-(-r,x)$ from the incomplete Gamma function $\gamma(-r,x)$ for negative integers. We then evaluate some convolutions and neutrix convolutions of these distributions and the functions $(x^s)_+$, $(x^s)_-$ and $x^s$.