The authors study the scalar delay-differential equation \[ \dot{x}(t) = B x(t - r), \qquad x(t) = C \text{ for } \quad t \in [-r,0], \] where \(r>0\) is the delay, and \(B, C\) are real numbers. Since the initial value is constant, the restriction \(x_n\) of the solution \(x\) on \(\left[(n-1) r, n r \right]\) is a polynomial of degree at most \(n\): \[ x_n(t) = \sum_{j=0}^n w^n_j t^j. \] In the main theorem, the authors provide a formula for the \(w^n_j\) that doesn’t require the recursive computation that the classic method of steps would entail. However, the argument is not totally convincing since – if one considers another polynomial basis – this recursion can actually be solved very simply. Indeed, with \(r = 1\) and \(C=1\), we have \[ x_n(t) = \sum_{j=0}^n \frac{B^j}{j!}(t-j+1)^j \] and the general case can be deduced easily from this one.