# Reciprocal of delta exponential

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## Theorem

Let $\mathbb{T}$ be a time scale, let $t,s \in \mathbb{T}$, and let $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be a regressive function. The following formula holds: $$\dfrac{1}{e_p(t,s;\mathbb{T})}=e_{\ominus p}(s,t;\mathbb{T}),$$ where $e_p$ denotes the delta exponential and $\ominus$ denotes circle minus.