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Math overflow question on fractional exponential iterations
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(03/28/2018, 07:57 PM)sheldonison Wrote: ... Let a and b be real numbers above e^{1/e}, and c<d be real numbers.  Do we have 
Another observation is that if c=1, c<d then limit holds for all versions of tetration, even if a<b, assuming the derivative is strictly increasing.  If c=d=1, and a<b, then we would have 

but if  so d is a little bit bigger than c=1, then eventually for large enough values of x even though a<b.
but only if x is big enough when a<b.
I think I could come up with an approximation for how big x has to be for this equation to hold.

This line of reasoning sheds some light on the general question which includes when c<>1, and helps one understand why Walker's solution works.
- Sheldon
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RE: Math overflow question on fractional exponential iterations - by sheldonison - 03/29/2018, 10:13 PM

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