On the Non-commutative Neutrix Product of the Distributions δ ⁽ʳ⁾(x) and x⁻ˢlnᵐ|x|}

It is proved that the non-commutative neutrix product of the distributions δ ⁽ʳ⁾(x) and x⁻ˢ lnᵐ|x| exists and δ ⁽ʳ⁾(x) ∘ x⁻ˢ lnᵐ |x| = 0 for r,m=0,1,2, … and s = 1,2, …. 2000 Mathematics Subject Classification. 46F10