Difference between revisions of "Jackson logarithm"
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| − | + | Let $\mathbb{T}$ be a time scale. Let $p \in \mathcal{R}(\mathbb{T},\mathbb{R})$ be [[regressive_function | regressive]]. Let $g \colon \mathbb{T} \rightarrow \mathbb{R}$ be nonvanishing. Define the Jackson logarithm of $g$ by | |
$$\log_{\mathbb{T}}g(t)=\dfrac{g^{\Delta}(t)}{g(t)}.$$ | $$\log_{\mathbb{T}}g(t)=\dfrac{g^{\Delta}(t)}{g(t)}.$$ | ||
| + | |||
| + | =Properties= | ||
| + | [[Jackson logarithm of delta exponential]]<br /> | ||
| + | [[Delta exponential of Jackson logarithm]]<br /> | ||
| + | [[Jackson logarithm of a product]]<br /> | ||
| + | |||
| + | =See also= | ||
| + | [[Bohner logarithm]]<br /> | ||
| + | [[Euler-Cauchy logarithm]]<br /> | ||
| + | [[Mozyrska-Torres logarithm]]<br /> | ||
| + | |||
| + | =References= | ||
| + | *{{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 $1.1$, $(1.1)$
