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. It is proved that the neutrix composition exists and for , where is the integer part of and the constants are defined by the expansion , for . Further results are also proved.
Brian Fisher. Adem Kılıçman. "On the Composition and Neutrix Composition of the Delta Function with the Hyperbolic Tangent and Its Inverse Functions." J. Appl. Math. 2011 1 - 13, 2011. https://doi.org/10.1155/2011/846736