# Difference between revisions of "Euler-Cauchy logarithm"

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− | Let $\mathbb{T}$ be a [[time scale]]. | + | 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]]<br /> |

− | + | [[Jackson logarithm]]<br /> | |

− | + | [[Mozyrska-Torres logarithm]]<br /> | |

=References= | =References= | ||

− | + | *{{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

- 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)