Difference between revisions of "Euler-Cauchy logarithm"

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=References=
 
=References=
 
*{{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}}: $(2)$
 +
{{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}}

Latest revision as of 15:30, 21 October 2017

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

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