# Difference between revisions of "Jackson logarithm"

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− | *{{PaperReference|The time scale logarithm|2008|Billy Jackson|next=Jackson logarithm of delta exponential}}: Definition 1.1, $(1.1)$ | + | *{{PaperReference|The time scale logarithm|2008|Billy Jackson|next=Jackson logarithm of delta exponential}}: Definition $1.1$, $(1.1)$ |

## Latest revision as of 17:43, 11 February 2017

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 $1.1$, $(1.1)$