Difference between revisions of "Bohner logarithm"
From timescalewiki
| Line 1: | Line 1: | ||
| − | 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 |
$$L_p(t,t_0) = \displaystyle\int_{t_0}^t \dfrac{p^{\Delta}(\tau)}{p(\tau)} \Delta \tau.$$ | $$L_p(t,t_0) = \displaystyle\int_{t_0}^t \dfrac{p^{\Delta}(\tau)}{p(\tau)} \Delta \tau.$$ | ||
Revision as of 23:27, 10 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
References
Martin Bohner: The logarithm on time scales (2005)... (previous)... (next): (3)
