# Difference between revisions of "Jackson logarithm"

From timescalewiki

(→Properties) |
|||

Line 5: | Line 5: | ||

[[Jackson logarithm of delta exponential]]<br /> | [[Jackson logarithm of delta exponential]]<br /> | ||

[[Delta exponential of Jackson logarithm]]<br /> | [[Delta exponential of Jackson logarithm]]<br /> | ||

+ | [[Jackson logarithm of a product]]<br /> | ||

=See also= | =See also= |

## Revision as of 17:37, 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)... (previous)... (next): Definition 1.1, $(1.1)$