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Searching for an asymptotic to exp[0.5]
#11
(05/12/2014, 03:48 PM)JmsNxn Wrote: I'm not sure if this will help, but I know some about taylor series and can do some fractional calculus Smile (Where can't we do fractional calculus)


If is holo on and satisfies some fast growth at imaginary infinity and negative infinity. And if in the half plane. Then fix :




Maybe that might help some of you? The unfortunate part is as we're going to get decay to zero. I'm not sure about the iterates. We can also note this is a modified fourier transform and so we can apply some of Paley Wiener's theorems on bounding fourier transforms from the original functions. I.e: We can bound the taylor series by the function in the integral. Therefore maybe if we get very fast decay to zero we can talk about asymptotics of .

Hey James,

Actually, the half iterate is really well behaved in the complex plane, if you follow the well behaved branch for real(z)>0, especially as compared to Tetration, so something like that should work. There are singularities at L, and at z+pi i, I need to remember where the singularities are; Mike has done a nice complex plane plot where if you put the branches at L, The singularity at L, L* are the only two singularities you see.
- Sheldon
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RE: Searching for an asymptotic to exp[0.5] - by sheldonison - 05/12/2014, 03:56 PM

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