> I still remember an old post by Mark D. Niemiec on that subject: > > [Jforum] Power in the Rational Domain > http://www.jsoftware.com/pipermail/general/2003-June/014722.html
You may want to look at "Fractional Calculus", https://en.wikipedia.org/wiki/Fractional_calculus , which make sense of things like that 1.25-th derivative and the 2.33-rd integral. On Thu, May 17, 2018 at 4:50 PM, Jose Mario Quintana < [email protected]> wrote: > Brian, > > No, I am afraid I was not trying to address your question. I was just > suggesting that a counterpart of the usual saying "the approximation breaks > down at that certain point" (dividing the real line) is "the approximation > breaks down at a certain line" (dividing the complex plane). > > Bob, > > I had seen before that video and I liked a lot. Whereas the domain > coloring grid (of isomagnitud and isophase lines) is a grid of the > transformation of the domain (the image), in that video what is shown is > the transformation a square grid (if I am not mistaken). One very appealing > feature of the video, at least for me, was the smooth transition from the > grid of the domain into the transformed grid corresponding to the image. I > can only guess the details how this was done. In my opinion, ideally, it > should be done by fractional powers in the sense of ^: (e.g., u^:1 -: > (u^:0.5)@:(u^:0.5) so to speak). I still remember an old post by Mark D. > Niemiec on that subject: > > [Jforum] Power in the Rational Domain > http://www.jsoftware.com/pipermail/general/2003-June/014722.html > > I am not sure if this approach would always work for analytical (continued) > functions. (I regret not having taken a complex variable course as an > optative in college.) > > > On Wed, May 16, 2018 at 1:13 PM, robert therriault <[email protected]> > wrote: > > > Pretty amazing visualization of what the zeta function is by Grant > > Sanderson. > > > > https://www.youtube.com/watch?v=sD0NjbwqlYw > > > > His videos are mathematically grounded and incredibly communicative in > the > > ways that they use animation and graphs. > > > > Cheers, bob > > > > > On May 16, 2018, at 9:45 AM, Brian Schott <[email protected]> > > wrote: > > > > > > Pepe, > > > > > > I was able to compare the "domain"-induced viewrgb with the wikipedia > > > version and I see the difference you noted. > > > Was that example an attempt at addressing my question about where lines > > of > > > finite length can be drawn for this case? > > > I ask that because you used the phrase "at that line". > > > > > > > > > On Tue, May 15, 2018 at 6:50 PM, Jose Mario Quintana < > > > [email protected]> wrote: > > > > > >> I am glad to hear that it runs on JQt/Linux. It also seems to run on > > JHS > > >> (at least it works with a Kindle Paperwhite 3 running on JHS/Linux > > >> (BusyBox) using a custom J interpreter). > > >> > > >> You might find the following clumsy verb useful, > > >> > > >> domain=. |.@|:@({.@[ + ] *~ j./&i.&>/@+.@(1j1 + ] %~ -~/@[))&>/ > > >> > > >> It produces the vertices of a square grid corresponding to (the lower > > and > > >> upper points of) a given complex interval and resolution; for example, > > >> > > >> In particular, > > >> > > >> viewrgb 12 ccEnhPh zetahat"0 domain _20j_30 20j30 ; 0.1 > > >> > > >> reproduces, to some extent, the first graph on the Wikipedia page for > > the > > >> Riemann zeta function. The leftmost section of the graph produced by > J > > >> looks suspicious and might indicate that Ewart's default approximation > > >> (zetahat) breaks down at that point (or rather, at that line). > > >> > > >> > > >> > > >> > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
