Jackson logarithm

Let $\mathbb{T}$ be a time scale. Let $p \in \mathcal{R}(\mathbb{T},\mathbb{R})$ be regressive. Let $g \colon \mathbb{T} \rightarrow \mathbb{R}$ be nonvanishing. Define the Jackson logarithm of $g$ by $$\log_{\mathbb{T}}g(t)=\dfrac{g^{\Delta}(t)}{g(t)}.$$

Properties

Jackson logarithm of delta exponential
Delta exponential of Jackson logarithm
Jackson logarithm of a product

See also

Bohner logarithm
Euler-Cauchy logarithm
Mozyrska-Torres logarithm

References

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