• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Super-root 3 andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 01/12/2016, 05:07 AM (This post was last modified: 01/12/2016, 05:12 AM by andydude.) (01/10/2016, 06:46 PM)sheldonison Wrote: How fast does the superroot3 grow on the negative real axis? Something funny happens somewhere near -35.83, maybe because the imaginary part goes to zero. Is this another singularity, or an exponential/logarithmic branch problem? z = -0.368593375973251 + 8.24287825516783 E-7*I z^z^z = -35.83 z = -0.36859401116538 z^z^z = -35.830698526398 I think I know what is going on here. Firstly, it appears that if we use the above branch cuts, then the imag(superroot_3(z)) would cross 0 around z = -36.         Secondly, the reason why this creates a discontinuity is that this corresponds to a branch cut of superpower_3 (also known as z^z^z):     You can kind of think of traveling along the negative real axis in superroot_3 is like traveling the cyan (light blue) region in superpower_3. The dot in the plot above is approximately where the value of superpower_3 == -64, and the point would be the value of superroot_3(-64) if it was continuous, but you won't get this value on the main branch of superpower_3, because by traveling along the negative real axis of superroot_3, you've crossed a branch cut of superpower_3. In order to make that region continuous, then you would have to choose a branch of superpower_3 that is continuous with the upper-left quadrant for the "green region" above, and choose a branch of superpower_3 that is continuous with lower-left quadrant for the "blue region" above. So in order to calculate the roots of z^z^z, we need a way to choose branches of it... « Next Oldest | Next Newest »

 Messages In This Thread Super-root 3 - by andydude - 01/03/2016, 07:45 PM RE: Super-root 3 - by andydude - 01/10/2016, 08:14 AM RE: Super-root 3 - by andydude - 01/10/2016, 05:41 PM RE: Super-root 3 - by sheldonison - 01/10/2016, 06:46 PM RE: Super-root 3 - by andydude - 01/12/2016, 05:07 AM RE: Super-root 3 - by andydude - 01/12/2016, 08:52 AM RE: Super-root 3 - by andydude - 01/12/2016, 09:10 AM RE: Super-root 3 - by andydude - 01/17/2016, 08:26 PM RE: Super-root 3 - by sheldonison - 01/18/2016, 02:40 AM RE: Super-root 3 - by andydude - 01/18/2016, 05:28 AM RE: Super-root 3 - by andydude - 01/19/2016, 03:14 AM

 Possibly Related Threads... Thread Author Replies Views Last Post Is bugs or features for fatou.gp super-logarithm? Ember Edison 10 4,111 08/07/2019, 02:44 AM Last Post: Ember Edison A fundamental flaw of an operator who's super operator is addition JmsNxn 4 7,506 06/23/2019, 08:19 PM Last Post: Chenjesu Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 4,769 06/10/2019, 04:29 AM Last Post: Ember Edison Inverse super-composition Xorter 11 14,351 05/26/2018, 12:00 AM Last Post: Xorter The super 0th root and a new rule of tetration? Xorter 4 4,558 11/29/2017, 11:53 AM Last Post: Xorter Solving tetration using differintegrals and super-roots JmsNxn 0 2,128 08/22/2016, 10:07 PM Last Post: JmsNxn The super of exp(z)(z^2 + 1) + z. tommy1729 1 2,880 03/15/2016, 01:02 PM Last Post: tommy1729 super of exp + 2pi i ? tommy1729 1 3,691 08/18/2013, 09:20 PM Last Post: tommy1729 Principal Branch of the Super-logarithm andydude 7 14,630 06/20/2011, 09:32 PM Last Post: tommy1729 e is the global maximum of x root x, 2 root 2 = 4 root 4, so... robo37 4 6,441 02/15/2011, 05:08 PM Last Post: bo198214

Users browsing this thread: 1 Guest(s)