Difference between revisions of "Bohner logarithm"
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| − | Let $\mathbb{T}$ be a [[time scale]] and let $p \mathbb{T} \rightarrow \mathbb{C}$ [[delta derivative|delta differentiable]]. The Bohner logarithm is defined by | + | Let $\mathbb{T}$ be a [[time scale]] and let $p \colon \mathbb{T} \rightarrow \mathbb{C}$ [[delta derivative|delta differentiable]]. The Bohner logarithm is defined by |
$$L_p(t,t_0) = \displaystyle\int_{t_0}^t \dfrac{p^{\Delta}(\tau)}{p(\tau)} \Delta \tau.$$ | $$L_p(t,t_0) = \displaystyle\int_{t_0}^t \dfrac{p^{\Delta}(\tau)}{p(\tau)} \Delta \tau.$$ | ||
=Properties= | =Properties= | ||
[[Bohner logarithm sub a product]]<br /> | [[Bohner logarithm sub a product]]<br /> | ||
| + | |||
| + | =See also= | ||
| + | [[Euler-Cauchy logarithm]]<br /> | ||
| + | [[Jackson logarithm]]<br /> | ||
| + | [[Mozyrska-Torres logarithm]]<br /> | ||
=References= | =References= | ||
| − | {{PaperReference|The logarithm on time scales|2005|Martin Bohner|prev= | + | *{{PaperReference|The logarithm on time scales|2005|Martin Bohner|prev=Euler-Cauchy logarithm}}: $(3)$ |
Latest revision as of 17:02, 11 February 2017
Let $\mathbb{T}$ be a time scale and let $p \colon \mathbb{T} \rightarrow \mathbb{C}$ delta differentiable. The Bohner logarithm is defined by $$L_p(t,t_0) = \displaystyle\int_{t_0}^t \dfrac{p^{\Delta}(\tau)}{p(\tau)} \Delta \tau.$$
Properties
Bohner logarithm sub a product
See also
Euler-Cauchy logarithm
Jackson logarithm
Mozyrska-Torres logarithm
