Let be a distribution in and let be a locally summable function. The composition of and is said to exist and be equal to the distribution if the limit of the sequence is equal to , where for and is a certain regular sequence converging to the Dirac delta function. In the ordinary sense, the composition does not exists. In this study, it is proved that the neutrix composition exists and is given by , for and , where . Further results are also proved.
Brian Fisher. Adem Kılıçman. "On the Neutrix Composition of the Delta and Inverse Hyperbolic Sine Functions." J. Appl. Math. 2011 1 - 12, 2011. https://doi.org/10.1155/2011/612353