by FrediFizzx » Tue Oct 27, 2015 4:53 pm
Joy Christian wrote:***
It is worth noting here that, in the context of the equations (5) and (6) of the above paper, the following more general identity of limits also holds:
\,{\bf L}({\bf s},\,\lambda^k)\right\}\bigg]\bigg[\lim_{{\bf s}\,\rightarrow\,{\bf b'}}\left\{\,+\,{\bf L}({\bf s},\,\lambda^k)\,{\bf D}({\bf b})\right\}\,\right]\bigg]\;=\;\lim_{\substack{{\bf s}\,\rightarrow\,{\bf a'} \\ {\bf s}\,\rightarrow\,{\bf b'}}}\big\{\,-\,{\bf D}({\bf a})\,{\bf L}({\bf s},\,\lambda^k)\,\,{\bf L}({\bf s},\,\lambda^k)\,{\bf D}({\bf b})\,\big\}.)
It is quite easy to verify this identity of limits. Alternatively, one can just look up the general properties of limits in a good schoolbook on calculus.
***
Perhaps the notation you are using on the RHS might be messing up some people? I think usually it is something like s --> (a', b') or would it be (s, s) --> (a', b')?
http://tutorial.math.lamar.edu/Classes/ ... imits.aspxAnyways, it is perfectly understandable what you are doing either way.
[quote="Joy Christian"]***
It is worth noting here that, in the context of the equations (5) and (6) of the above paper, the following more general identity of limits also holds:
[tex]\bigg[\lim_{{\bf s}\,\rightarrow\,{\bf a'}}\left\{\,-\,{\bf D}({\bf a})\,{\bf L}({\bf s},\,\lambda^k)\right\}\bigg]\bigg[\lim_{{\bf s}\,\rightarrow\,{\bf b'}}\left\{\,+\,{\bf L}({\bf s},\,\lambda^k)\,{\bf D}({\bf b})\right\}\,\right]\bigg]\;=\;\lim_{\substack{{\bf s}\,\rightarrow\,{\bf a'} \\ {\bf s}\,\rightarrow\,{\bf b'}}}\big\{\,-\,{\bf D}({\bf a})\,{\bf L}({\bf s},\,\lambda^k)\,\,{\bf L}({\bf s},\,\lambda^k)\,{\bf D}({\bf b})\,\big\}.[/tex]
It is quite easy to verify this identity of limits. Alternatively, one can just look up the general properties of limits in a good schoolbook on calculus.
***[/quote]
Perhaps the notation you are using on the RHS might be messing up some people? I think usually it is something like s --> (a', b') or would it be (s, s) --> (a', b')?
http://tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx
Anyways, it is perfectly understandable what you are doing either way.
