Difference between revisions of "Mozyrska-Torres logarithm is positive on (1,infinity)"
From timescalewiki
(Created page with "==Theorem== Let $\mathbb{T}$ be a time scale. If $t \in (1,\infty) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) > 0$. ==Proof== ==References== {{PaperReference|The Natural Log...") |
|||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
==Theorem== | ==Theorem== | ||
| − | Let $\mathbb{T}$ be a time scale. If $t \in (1,\infty) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) > 0$. | + | Let $\mathbb{T}$ be a time scale. If $t \in (1,\infty) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) > 0$, where $L_{\mathbb{R}}$ denotes the Mozyrska-Torres logarithm. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| − | {{PaperReference|The Natural Logarithm on Time Scales| | + | {{PaperReference|The Natural Logarithm on Time Scales|2008|Dorota Mozyrska|author2 = Delfim F. M. Torres|prev=Mozyraska-Torres logarithm is negative on (0,1)|next=Mozyrska-Torres logarithm composed with forward jump}} |
Revision as of 15:27, 21 October 2017
Theorem
Let $\mathbb{T}$ be a time scale. If $t \in (1,\infty) \cap \mathbb{T}$, then $L_{\mathbb{T}}(t) > 0$, where $L_{\mathbb{R}}$ denotes the Mozyrska-Torres logarithm.
Proof
References
Dorota Mozyrska and Delfim F. M. Torres: The Natural Logarithm on Time Scales (2008)... (previous)... (next)
