Difference between revisions of "Delta derivative of Mozyrska-Torres logarithm"
From timescalewiki
(Created page with "==Theorem== Let $\mathbb{T}$ be a time scale including $1$ and at least one other point $t$ such that $0< t < 1$. The following formula holds: $$L_{\mathbb{T}}^{\Delta}(t) = \...") |
|||
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
==Theorem== | ==Theorem== | ||
Let $\mathbb{T}$ be a time scale including $1$ and at least one other point $t$ such that $0< t < 1$. The following formula holds: | Let $\mathbb{T}$ be a time scale including $1$ and at least one other point $t$ such that $0< t < 1$. The following formula holds: | ||
| − | $$L_{\mathbb{T}}^{\Delta}(t) = \dfrac{1}{t} | + | $$L_{\mathbb{T}}^{\Delta}(t) = \dfrac{1}{t},$$ |
| + | where $L_{\mathbb{T}}$ denotes the [[Mozyrska-Torres logarithm]]. | ||
| + | |||
| + | ==Proof== | ||
| + | |||
| + | ==References== | ||
| + | {{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyrska-Torres logarithm|next=Mozyrska-Torres logarithm at 1}} | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 15:28, 21 October 2017
Theorem
Let $\mathbb{T}$ be a time scale including $1$ and at least one other point $t$ such that $0< t < 1$. The following formula holds: $$L_{\mathbb{T}}^{\Delta}(t) = \dfrac{1}{t},$$ where $L_{\mathbb{T}}$ denotes the Mozyrska-Torres logarithm.
Proof
References
Dorota Mozyrska and Delfim F. M. Torres: The Natural Logarithm on Time Scales (2008)... (previous)... (next)
