On the Non-Commutative Neutrix Convolution of $\tan^{-1}x$ and $x^{r}$


Mongkolsery Lin, Brian Fisher, Somsak Orankitjaroen




We define regular distributions $\tan_{+}^{-1}x$ and $\tan_{-}^{-1}x$ from the function $\tan^{-1}x$. We then evaluate some convolutions and neutrix convolutions of these distributions and the functions $x_{+}^{r}$, $x_{-}^{r}$ and $x^{r}$.