Semigroup property of delta exponential

Theorem

Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $p \in \mathcal{R}\left( \mathbb{T},\mathbb{C} \right)$ be a forward regressive function. The following formula holds for all $s,t \in \mathbb{T}$: $$e_p(t,r;\mathbb{T})e_p(r,s;\mathbb{T})=e_p(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential.

References

• Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Lemma $2.31$