Difference between revisions of "Mozyrska-Torres logarithm"

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[http://arxiv.org/pdf/0809.4555.pdf Mozyrska, Dorota; Torres, Delfim F. M. The natural logarithm on time scales. J. Dyn. Syst. Geom. Theor. 7 (2009), no. 1, 41--48.]
{{PaperReference|The Natural Logarithm on Time Scales|2009|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=findme|next=findme}}: page 1

Revision as of 20:52, 17 September 2016

Let $\mathbb{T}$ be a time scale. For $t \in \mathbb{T} \cap (0,\infty)$, define $$L_{\mathbb{T}}(t) = \displaystyle\int_1^t \dfrac{1}{\tau} \Delta \tau.$$


  • $L^{\Delta}_{\mathbb{T}}(t) = \dfrac{1}{t}$
  • $L_{\mathbb{T}}(1)=0$
  • $L_{\mathbb{R}}(t)=\log(t)$
  • $L_{\mathbb{T}}(\cdot)$ is increasing and continuous
  • $L_{\mathbb{T}}(\sigma(t))=L_{\mathbb{T}}(t)+\mu(t)L_{\mathbb{T}}^{\Delta}(t)=L_{\mathbb{T}}(t)+\dfrac{\mu(t)}{t}$


Dorota Mozyrska and Delfim F. M. Torres: The Natural Logarithm on Time Scales (2009)... (previous)... (next): page 1