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Is the following expression for tetration useful?
#6
No problem. I know it doesn't converge for e^s because its exponential derivative doesn't approach zero fast enough as it goes to negative infinity. It stays constant. So what we say is e^s is non-integral analytic.

Sorry should have said that. We can also solve for:



or any function that grows fast enough.
and find:



My guess is that it is integral analytic; (i.e; converges for some s in this expression); but I haven't proved that.
Basically this manipulation works on functions that grow a certain rate. I'm going to try and prove what that rate is regarding that I have to take the integral transformations into consideration.


I actually prefer this only being on this website until I write the paper. I tend to get over anxious and post things that I forget to check. Does this make more sense at what I was trying to get at? I'm more interested in the fact that I have an integral expression for the inverse of the iterated Riemann-Liouville differintegral.


I just didn't want to say that out-loud Tongue The point of having expressions for is that I can express multiplication and addition.
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RE: Is the following expression for tetration useful? - by JmsNxn - 11/08/2012, 02:40 PM

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