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 Is the following expression for tetration useful? JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 11/08/2012, 02:40 PM (This post was last modified: 11/08/2012, 02:49 PM by JmsNxn.) 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: $\mathcal{E} e^{e^s} = g(s)$ or any function $f$ that grows fast enough. and find: $e^{e^s} = \int_{-\infty}^{\infty} g(t) \frac{s^t}{\Gamma(t+1)}\,\partial t$ 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 The point of having expressions for $e^s, \sin(s),...$ is that I can express multiplication and addition. « Next Oldest | Next Newest »

 Messages In This Thread Is the following expression for tetration useful? - by JmsNxn - 11/07/2012, 08:23 PM RE: Is the following expression for tetration useful? - by mike3 - 11/07/2012, 09:19 PM RE: Is the following expression for tetration useful? - by JmsNxn - 11/07/2012, 10:11 PM RE: Is the following expression for tetration useful? - by mike3 - 11/07/2012, 10:38 PM RE: Is the following expression for tetration useful? - by mike3 - 11/07/2012, 10:52 PM RE: Is the following expression for tetration useful? - by JmsNxn - 11/08/2012, 02:40 PM RE: Is the following expression for tetration useful? - by mike3 - 11/10/2012, 03:19 AM RE: Is the following expression for tetration useful? - by tommy1729 - 11/13/2012, 11:50 PM RE: Is the following expression for tetration useful? - by tommy1729 - 11/12/2012, 04:12 PM RE: Is the following expression for tetration useful? - by tommy1729 - 11/14/2012, 11:29 PM

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