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Tetration extension for bases between 1 and eta
(11/07/2009, 11:30 PM)dantheman163 Wrote: If we set which is to say

then reduce it to

Then just strait up plug in infinity for k
we get which is the same as

Slowly, slowly. The first line is what you want to show. You show from the first line something true, but you can also show something true starting from something wrong; so thats not sufficient. Also it seems as if you confuse limit equality with sequence equality.

Lets have a look at the inverse function ,
it should satisfy

Then lets compute

Take for example then the right side converges to the derivative of at the fixed point; and not to 1 as it should be.

This is the reason why the formula is only valid for functions that have derivative 1 at the fixed point, e.g. , i.e. .

Quote:This is really weird because if i do for
i get about 1.558 which is substantially larger then

Can anyone else confirm that for ?

Try the same with and it will work; but for no other base; except you use the modified formula I described before.

Messages In This Thread
RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/08/2009, 02:44 PM

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