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 Real and complex behaviour of the base change function (was: The "cheta" function) jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 08/17/2009, 05:26 PM (08/17/2009, 04:01 PM)sheldonison Wrote: I wanted to step back to the base conversion equation, in the strip where $\text{sexp_\eta(x)$ varies from 4.38 to 5.02, which would correspond more or less to sexp_e=0 to 1. The hope was to extend such a strip to the complex plane. I wanted to share a few observations about the singularities in this strip, where z = $\text{slog_\eta(5.02)$. Here f(z)=1, which corresponds to sexp_e(0).Just a quick observation, to make sure we are speaking of the same thing. When converting from base eta to base e, I find that 5.0179 goes to 0, not 1, and which corresponds with sexp(-1), not sexp(0). I get confused sometimes when I work with exp(z)-1 instead of actually working with the iterations of eta^z, and sometimes I forget to switch properly between the two. Perhaps you are making the same mistake? A quick sanity check in SAGE is: Code:eta = RR(e**(1/e)); print log(log(log(log(log(eta**(eta**(eta**(eta**(eta**5.0179)))))))));You should get something like -0.000053416. I try to remember that 5.0179 goes to 0, and 6.3344 goes to 1, and then always double check my results inside my iterating functions. If not, it's usually because I am still working in a logarithmic or double logarithmic system. It's a moot point, for the most part, because it's a trivial shift in the sexp function, but I wanted to make sure it got caught early before you start getting results that don't match mine, and we can't figure out why! ~ Jay Daniel Fox « Next Oldest | Next Newest »

 Messages In This Thread Real and complex behaviour of the base change function (was: The "cheta" function) - by bo198214 - 08/12/2009, 08:59 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function) - by jaydfox - 08/15/2009, 12:54 AM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/15/2009, 05:00 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by bo198214 - 08/15/2009, 05:36 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/15/2009, 06:40 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/15/2009, 07:13 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by bo198214 - 08/15/2009, 09:44 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/15/2009, 10:40 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/15/2009, 10:46 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/15/2009, 11:02 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/15/2009, 11:20 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by bo198214 - 08/16/2009, 11:15 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/16/2009, 11:38 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by bo198214 - 08/17/2009, 08:50 AM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/17/2009, 12:07 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by sheldonison - 08/17/2009, 04:01 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by bo198214 - 08/17/2009, 04:30 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/17/2009, 05:26 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by sheldonison - 08/18/2009, 04:37 AM RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/17/2009, 05:47 PM RE: Real and complex behaviour of the base change function (was: The "cheta" function) - by bo198214 - 08/17/2009, 02:40 PM base change with decremented exponential - by bo198214 - 08/18/2009, 08:47 AM singularities of base change eta -> e - by bo198214 - 08/18/2009, 06:51 PM RE: singularities of base change eta -> e - by bo198214 - 08/20/2009, 10:28 AM RE: Does the limit converge in the complex plane? - by sheldonison - 08/13/2009, 12:49 AM RE: Does the limit converge in the complex plane? - by bo198214 - 08/13/2009, 07:17 AM RE: Does the limit converge in the complex plane? - by sheldonison - 08/13/2011, 10:32 AM RE: Does the limit converge in the complex plane? - by bo198214 - 08/13/2011, 06:33 PM RE: Does the limit converge in the complex plane? - by sheldonison - 08/13/2009, 06:48 PM

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