Singularity functions

define $$\mu_{i+1} = \int_{-\infty}^t \mu_i(\lambda - t) d\lambda$$ where $\mu_0(t) = \delta(t)$, i.e. δ-function or unit impulse,

and, $\mu_1(t) = 1(t)$, i.e. Step function

References

1. Sarachik - Principles of linear systems, 1997, p 43
2. https://en.wikipedia.org/wiki/Singularity_function