Funny pictures of sexps
#22
(08/25/2009, 09:43 PM)jaydfox Wrote: Henryk, I've found some rather bizarre behvior with your method of shifting the Abel function's center. For example, it seems fairly well behaved for real shifts, but even a small imaginary shift seems to produce garbage results (i.e., as I increase the matrix size, I don't get convergence, but rather rapid divergence).
Well its not shifting of the Abel function (see my post before).
But this is indeed strange, the only thing I can say that I would expect the complex shift yielding complex values on the real axis, thatswhy I didnt try it.

Quote:I can use complex math with f(x)=e*(x+x0)-x0 to get the power series for log(x+x0), except the leading constant term of course. This holds true for each value of x0 I have tried so far, including complex values or pure imaginary values.
And now prove it! Wink
I could already show that the result does not depend on x0 (hopefully its on the forum), but not that it is log.

Quote:However, I was unable to successfully recenter the islog_e to x=0.25*i, which is a very small shift, relatively speaking. Why should we be unable to shift away from the real axis, if we are not limited by a radius of convergence?
As I said, its not a shift of the Abel function but the result may be a different Abel function. I dont know about the mechanisms of its convergence. Proof of convergence of the intuitive method is anyway still open.


Messages In This Thread
Funny pictures of sexps - by bo198214 - 08/25/2009, 01:56 AM
RE: Funny pictures of sexps - by bo198214 - 08/25/2009, 03:59 PM
RE: Funny pictures of sexps - by jaydfox - 08/25/2009, 04:24 PM
RE: Funny pictures of sexps - by bo198214 - 08/25/2009, 05:09 PM
RE: Funny pictures of sexps - by jaydfox - 08/25/2009, 05:43 PM
RE: Funny pictures of sexps - by bo198214 - 08/25/2009, 06:01 PM
RE: Funny pictures of sexps - by bo198214 - 08/25/2009, 08:50 PM
RE: Funny pictures of sexps - by bo198214 - 08/25/2009, 09:39 PM
RE: Funny pictures of sexps - by jaydfox - 08/25/2009, 09:59 PM
RE: Funny pictures of sexps - by jaydfox - 08/25/2009, 09:43 PM
RE: Funny pictures of sexps - by bo198214 - 08/25/2009, 09:55 PM
RE: Funny pictures of sexps - by jaydfox - 08/25/2009, 10:02 PM
RE: Funny pictures of sexps - by jaydfox - 08/25/2009, 10:23 PM
RE: Funny pictures of sexps - by bo198214 - 08/26/2009, 10:23 AM
RE: Funny pictures of sexps - by jaydfox - 08/26/2009, 07:21 PM
RE: Funny pictures of sexps - by bo198214 - 08/26/2009, 08:08 PM
RE: Funny pictures of sexps - by jaydfox - 08/26/2009, 08:38 PM
RE: Funny pictures of sexps - by bo198214 - 08/26/2009, 09:15 PM
RE: Funny pictures of sexps - by bo198214 - 08/26/2009, 09:28 PM
RE: Funny pictures of sexps - by bo198214 - 08/26/2009, 09:36 PM
RE: Funny pictures of sexps - by jaydfox - 08/26/2009, 09:55 PM
RE: Funny pictures of sexps - by bo198214 - 08/26/2009, 10:26 PM
RE: Funny pictures of sexps - by jaydfox - 08/26/2009, 11:00 PM
RE: Funny pictures of sexps - by jaydfox - 08/26/2009, 09:02 PM
RE: Funny pictures of sexps - by bo198214 - 08/26/2009, 05:46 PM
RE: Funny pictures of sexps - by jaydfox - 08/26/2009, 08:11 PM
RE: Funny pictures of sexps - by bo198214 - 08/27/2009, 02:51 PM
RE: Funny pictures of sexps - by jaydfox - 08/27/2009, 04:38 PM
RE: Funny pictures of sexps - by jaydfox - 08/27/2009, 04:58 PM
RE: Funny pictures of sexps - by bo198214 - 08/27/2009, 05:43 PM
RE: Funny pictures of sexps - by bo198214 - 08/27/2009, 05:36 PM
RE: Funny pictures of sexps - by jaydfox - 08/27/2009, 06:21 PM
RE: Funny pictures of sexps - by bo198214 - 08/27/2009, 06:52 PM
RE: Funny pictures of sexps - by bo198214 - 08/25/2009, 10:20 PM

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