Some results on the neutrix composition of the delta function (Q2867613)

Neutrix calculus has been introduced by \textit{J. G. van der Corput} [J. Anal. Math. 7, 281--398 (1960; Zbl 0097.10503)] as a technique which gives meaning to certain divergent sums or integrals, by neglecting appropriate quantities. The authors contributed to the study of various aspects of neutrix calculus through many papers in the last two decades. In this paper, they discuss the existence of the composition \(\delta^{(s)}\{[\exp_+(x)-H(x)]^{1/r}\}\) when \(r=1,2,\dots\) and \(s=0,1,2,\dots\) and, in particular, derive the formula NEWLINE\[NEWLINE \delta^{(mr-1)}\{[\exp_+(x)-H(x)]^{1/r}\}= \sum_{k=0}^{m-1}\frac{(-1)^{mr+k-1}r(mr-1)!c_{mr-1,k}}{2k!}\delta^{(k)}(x)NEWLINE\]NEWLINE for \(m,r=1,2,\dots\).