Difference between revisions of "Mozyrska-Torres logarithm composed with forward jump"

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(Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. Then, $$L_{\mathbb{T}}(\sigma(t)) = L_{\mathbb{T}}(t) + \dfrac{\mu(t)}{t},$$ where $L_{\mathbb{T}}$ denotes the Mozyrska-To...")
 
 
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==References==
 
==References==
{{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyraska-Torres logarithm is positive on (1,infinity)|next=Euler-Cauchy logarithm}}
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{{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm is positive on (1,infinity)|next=Euler-Cauchy logarithm}}

Latest revision as of 15:31, 21 October 2017

Theorem

Let $\mathbb{T}$ be a time scale. Then, $$L_{\mathbb{T}}(\sigma(t)) = L_{\mathbb{T}}(t) + \dfrac{\mu(t)}{t},$$ where $L_{\mathbb{T}}$ denotes the Mozyrska-Torres logarithm, $\sigma$ denotes the forward jump, and $\mu$ denotes the forward graininess.

Proof

References

Dorota Mozyrska and Delfim F. M. Torres: The Natural Logarithm on Time Scales (2008)... (previous)... (next)