Delta exponential of Jackson logarithm

Theorem

Let $\mathbb{T}$ be a time scale. The following formula holds: $$e_{\log_{\mathbb{T}} f}(t,s)=\dfrac{f(t)}{f(s)},$$ where $e_{\cdot}$ denotes the delta exponential and $\log_{\mathbb{T}}$ denotes the Jackson logarithm.

References

• Billy Jackson: The time scale logarithm (2008)... (previous)... (next): Theorem $1.1$, $(1.3)$