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elementary superfunctions
#1
Triggered by the interesting finding of Andrew I open this thread for the further investigation of elementary superfunctions, i.e. functions that are expressible with elementary functions and operations such that

for a given elementary function .

Our first example is:
with a superfunction .

Now the has the same property as the . Hence is another superfunction of .

Indeed exists and is differentiable at .
But it does not exist at the other fixed point , because is not defined.

Edit: both are regular super-functions at fixed point 1. .

So if we are at polynomials , we can also give an elementary superfunction for , i.e. .
Because .

Edit: these are the regular super-exponentials at 1. .

Generally for Chebyshev polynomials, these are the polynomials such that - for example above we used -, we know already two elementary superfunctions of , these are and .
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Messages In This Thread
elementary superfunctions - by bo198214 - 04/23/2009, 01:25 PM
RE: elementary superfunctions - by bo198214 - 04/23/2009, 02:23 PM
RE: elementary superfunctions - by bo198214 - 04/23/2009, 03:46 PM
RE: elementary superfunctions - by tommy1729 - 04/27/2009, 11:16 PM
RE: elementary superfunctions - by bo198214 - 04/28/2009, 08:33 AM
RE: elementary superfunctions - by bo198214 - 03/27/2010, 10:27 PM
RE: elementary superfunctions - by bo198214 - 04/18/2010, 01:17 PM
RE: elementary superfunctions - by tommy1729 - 04/18/2010, 11:10 PM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 08:22 AM
RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 09:11 AM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 09:23 AM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 10:48 AM
RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 11:35 AM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 12:12 PM
RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 12:42 PM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 01:10 PM
RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 01:52 PM
Super-functions - by Kouznetsov - 05/11/2009, 02:02 PM
[split] open problems survey - by tommy1729 - 04/25/2010, 02:34 PM
RE: [split] open problems survey - by bo198214 - 04/25/2010, 05:15 PM

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