• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Notations and Opinions bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 04/09/2008, 11:30 AM (This post was last modified: 04/09/2008, 11:33 AM by bo198214.) We have a bit of a dilemma here. Though the ^n has advantages with respect to applying the \ and / notation, basicly its ambiguous with taking the n-th power. f^n(x) = f(x)f(x)....f(x) or f^n(x)=f(f(...f(x)...)). Of course you can say we can write the first one as f(x)^n, however then there is no operation to denote the n-th power of a function. So we need a different symbol instead of ^. For example in maple there is this notation with $n when taking the nth derivative with respect to x, you write diff(f,x$n). So I propose - if we want to give up the notation for the advantage of taking (\ and) / - f$n=$f^{\circ n}$. correspondingly b[k]$n(x), b/[k]$n(x), etc as you already listed. As now the$ is available because we have the notation [4] and [5] and dont need dedicated symbols like #, \$ or § for them anymore. Quote:Fortunately, however, we do not need a notation for auxiliary hyper-logarithms, because: $h = \mathtt{b[N]\^{\backslash}z(x)} = \left({}^N_b\begin{tabular}{|c} z \\\hline\end{tabular}\right) - \left({}^N_b\begin{tabular}{|c} x \\\hline\end{tabular}\right)$ So if neccessary, this can be written $h = \mathtt{b[N]{\backslash}z - b[N]{\backslash}x}$ which means we really don't need either my notation, nor GFR's notation for auxiliary hyper-logarithms. Thats really clever and again reminds me on Szekeres consideration of the Abel function as an integral in "Scales of infinity and Abel's functional equation", 1984. « Next Oldest | Next Newest »

 Messages In This Thread Notations and Opinions - by andydude - 01/21/2008, 02:08 AM RE: Notations and Opinions - by Gottfried - 01/21/2008, 06:48 AM RE: Notations and Opinions - by GFR - 01/21/2008, 10:23 PM RE: Notations and Opinions - by andydude - 01/22/2008, 05:04 AM RE: Notations and Opinions - by Ivars - 01/22/2008, 08:27 AM RE: Notations and Opinions - by andydude - 01/22/2008, 07:04 PM RE: Notations and Opinions - by Ivars - 01/22/2008, 09:56 PM RE: Notations and Opinions - by GFR - 01/22/2008, 10:12 AM RE: Notations and Opinions - by Ivars - 01/22/2008, 12:57 PM RE: Notations and Opinions - by GFR - 01/22/2008, 05:47 PM My Notation - by James Knight - 03/25/2008, 07:58 PM Notation needed - by bo198214 - 03/26/2008, 02:26 PM RE: Notations and Opinions - by GFR - 03/30/2008, 12:51 AM RE: Notations and Opinions - by andydude - 03/30/2008, 05:12 AM RE: Notations and Opinions - by GFR - 04/04/2008, 01:20 PM RE: Notations and Opinions - by bo198214 - 04/04/2008, 01:24 PM RE: Notations and Opinions - by GFR - 04/04/2008, 09:53 PM RE: Notations and Opinions - by GFR - 04/05/2008, 08:26 AM RE: Notations and Opinions - by GFR - 04/08/2008, 10:52 AM RE: Notations and Opinions - by GFR - 04/08/2008, 03:31 PM RE: Notations and Opinions - by bo198214 - 04/08/2008, 04:22 PM RE: Notations and Opinions - by GFR - 04/09/2008, 05:10 PM RE: Notations and Opinions - by andydude - 04/08/2008, 09:04 PM RE: Notations and Opinions - by bo198214 - 04/09/2008, 11:30 AM RE: Notations and Opinions - by GFR - 04/10/2008, 09:15 PM

Users browsing this thread: 2 Guest(s)