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So we all know we can use fixed point to calculate iterations. Functions that converge to a real value, then using Schroeder's equation to compute it.

But, when the function converges to a oscillating pattern? When the upper limit and downwards limit converges, and it keeps oscillating between the 2 (like for \({^x}a\) when \(a\) is between \(0\) and \(e^{-e}\)), is there a way, an equation to compute it?

The only way I've found to do so, is with function that converge into the negative iterations and oscillates in the positive (or vice versa if you use the inverse function). You compute it on the converging side, then apply the inverse function, but it's kinda cheating...

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Shanghai46

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10/15/2023, 12:47 AM
(This post was last modified: 10/15/2023, 12:48 AM by leon.)
The best way is to converge on the function could be using a oscillating diagram or by tetrating the limit and the maximum of the equation until it's over.

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(10/15/2023, 12:47 AM)leon Wrote: The best way is to converge on the function could be using a oscillating diagram or by tetrating the limit and the maximum of the equation until it's over.

Ummmm......What?

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Shanghai46

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One way is using sin or cos

For instance

https://tetrationforum.org/showthread.php?tid=1622
Bo and Leo and others went into this in various places.

regards

tommy1729

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(10/15/2023, 11:17 PM)tommy1729 Wrote: One way is using sin or cos

For instance

https://tetrationforum.org/showthread.php?tid=1622

Bo and Leo and others went into this in various places.

regards

tommy1729

btw , the links are dead but just paste the (thread identifation numbers) tid numbers and you can get there !

( because the name of the domain changed )

regards

tommy1729

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10/16/2023, 03:11 PM
(This post was last modified: 10/16/2023, 03:11 PM by leon.)
(10/15/2023, 08:03 PM)Shanghai46 Wrote: (10/15/2023, 12:47 AM)leon Wrote: The best way is to converge on the function could be using a oscillating diagram or by tetrating the limit and the maximum of the equation until it's over.

Ummmm......What?

An oscillating diagram is a diagram that rough computes for you on both negative and positive and in-between so you don't even have to use it just plug in the numbers. An oscillating function changes from pos to neg if numbers are big enough so it's iterations will always have sign this means you can compute iterations by taking the maximum going backwards etc

Sorry if I was unclear