The Nash cascade is a sequence of $N$ linear stores in series, each having a residence time of $K$ time units. The resulting mathematical form of the Nash-cascade is:

$$h(t) = (t/K)^{N-1}*exp(\frac{(-t/K)}{(K*\Gamma(N))}$$

where $h(t)$ is the unit hydrograph in terms of a unit discharge and $\gamma$ is the gamma function $\gamma(N)=(N-1)!$ for integer values $N$. $N$ can also have rational values.