On the Composition of Distributionsx−sln|x|and|x|

Let F be a distribution and let f be a locallysummable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn(f)}, where Fn(x)=F(x)*δn(x) and {δn(x)} is a certain sequence ofinfinitely differentiable functions converging to the Dirac delta-function δ(x). The composition of the distributions x−sIn|x| and |x|μ is evaluated for s=1,2,…,μ>0 and μs≠1,2,…