# Jackson logarithm

From timescalewiki

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

# See also

Bohner logarithm

Euler-Cauchy logarithm

Mozyrska-Torres logarithm

# References

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