Delta derivative of Mozyrska-Torres logarithm

Theorem

Let $\mathbb{T}$ be a time scale including $1$ and at least one other point $t$ such that $0< t < 1$. The following formula holds: $$L_{\mathbb{T}}^{\Delta}(t) = \dfrac{1}{t},$$ where $L_{\mathbb{T}}$ denotes the Mozyrska-Torres logarithm.

References

Dorota Mozyrska and Delfim F. M. Torres: The Natural Logarithm on Time Scales (2009)... (previous)... (next)