Difference between revisions of "Mozyrska-Torres logarithm composed with forward jump"
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==References== | ==References== | ||
| − | {{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev= | + | {{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}} |
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)
