The noncommutative neutrix product of $x_{-}^{-s}\ln^mx_{-}$ and $x_{+}^{r}$

Abstract

In distribution theory, the product of two distributions can only be defined under certain conditions. In this paper, by using Fisher's definition, it is proved that if Gm,s(x) denotes the distribution ( ln m+1x-)(s), then the noncommutative neutrix product [Formula: see text] exists and [Formula: see text] for m, s ≥ 1, where [Formula: see text]. Related neutrix products are then deduced.