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Turkish Journal of Mathematics, vol.48, no.6, pp.1001-1023, 2024 (SCI-Expanded)
In this paper we concern further results of [32, 33] by using the method mainly related to the finite part of divergent integral, in fact, we consider the powers for positive integers of the composition of the Dirac delta function and an infinitely differentiable function having any number of distinct multiple roots which will be defined as the neutrix limit of the regular sequence $δ^k_n$(f (x)) . Moreover we show that the powers of the composition δ(f (x)) for negative integers can be also defined via neutrix settings. Some compositions as examples to better understand will be given.