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 Further observations on fractional calc solution to tetration JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 05/30/2014, 04:10 PM (This post was last modified: 05/30/2014, 04:16 PM by JmsNxn.) Hi, everyone. This is a continuation of my last thread http://math.eretrandre.org/tetrationforu...hp?tid=847 I don't have the time to explain too much now, but I realize a mistake I made and it causes for an inaccurate result. Take $0<\sigma <1$ $\frac{1}{2 \pi i} \int_{\sigma - i\infty}^{\sigma + i\infty} \G(s) \frac{w^{-s}}{(^{-s} e)}\,ds = \vartheta(-w)$ Quite remarkably: $\vartheta(-w) = \sum_{n=0}^\infty \frac{(-w)^n}{(^n e)n!} + k(w)$ where I've recently calculated that: $k(w) = \lim_{n\to\infty} \frac{w^n}{2 \pi i} \int_{\sigma - i\infty}^{\sigma + i \infty} \G(s-n) \frac{w^{-s}}{(^{n-s} e)}\,ds$ Where I have been unable to calculate if this converges to a limit. If it does, (and I think it does), we are good. I'm not sure if I can show recursion with this new transform but I'll try my best to work on this. We recall the important property, of recovering tetration: $[\frac{d^z}{dw^z} \vartheta(w)]_{w=0} = \frac{1}{^z e}$, for $\Re(z) > -1$ « Next Oldest | Next Newest »

 Messages In This Thread Further observations on fractional calc solution to tetration - by JmsNxn - 05/30/2014, 04:10 PM RE: Further observations on fractional calc solution to tetration - by tommy1729 - 05/30/2014, 09:58 PM RE: Further observations on fractional calc solution to tetration - by mike3 - 05/31/2014, 01:46 AM RE: Further observations on fractional calc solution to tetration - by tommy1729 - 05/31/2014, 08:30 PM RE: Further observations on fractional calc solution to tetration - by mike3 - 06/01/2014, 11:16 PM RE: Further observations on fractional calc solution to tetration - by JmsNxn - 06/04/2014, 03:11 AM RE: Further observations on fractional calc solution to tetration - by tommy1729 - 06/04/2014, 10:02 PM RE: Further observations on fractional calc solution to tetration - by mike3 - 06/04/2014, 11:55 PM RE: Further observations on fractional calc solution to tetration - by mike3 - 06/05/2014, 12:45 AM RE: Further observations on fractional calc solution to tetration - by JmsNxn - 06/05/2014, 01:17 AM RE: Further observations on fractional calc solution to tetration - by tommy1729 - 06/05/2014, 08:13 AM RE: Further observations on fractional calc solution to tetration - by tommy1729 - 06/05/2014, 12:25 PM RE: Further observations on fractional calc solution to tetration - by JmsNxn - 06/05/2014, 01:25 PM RE: Further observations on fractional calc solution to tetration - by tommy1729 - 06/05/2014, 08:54 PM

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