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Notations and Opinions
#36
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 <n> notation for the advantage of taking (\ and) / -

f$n=.
correspondingly
b[k]$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:


So if neccessary, this can be written 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.
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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



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