Difference between revisions of "Euler-Cauchy logarithm"
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{{PaperReference|The logarithm on time scales|2005|Martin Bohner|prev=Delta exponential dynamic equation|next=Bohner logarithm}}: $(2)$ | {{PaperReference|The logarithm on time scales|2005|Martin Bohner|prev=Delta exponential dynamic equation|next=Bohner logarithm}}: $(2)$ | ||
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{{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm composed with forward jump|next=findme}} | {{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm composed with forward jump|next=findme}} | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 15:14, 21 January 2023
Let $\mathbb{T}$ be a time scale and let $s \in \mathbb{T}$. The Euler-Cauchy logarithm is defined by the formula $$L(t,s)=\displaystyle\int_{s}^t \dfrac{1}{\tau + 2\mu(\tau)} \Delta \tau.$$
Properties
See also
Euler-Cauchy dynamic equation
Jackson logarithm
Mozyrska-Torres logarithm
References
Martin Bohner: The logarithm on time scales (2005)... (previous)... (next): $(2)$ Dorota Mozyrska and Delfim F. M. Torres: The Natural Logarithm on Time Scales (2008)... (previous)... (next)
