Thread Rating:
  • 1 Vote(s) - 3 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))
#31
Ivars Wrote:Im (W) = +- ipi/2

then branches k=-1 and k=+1 are accordingly

-i(pi/2 - 2pi) = - 5/2pi i ; +i(pi/2+2pi) = + 5/2 pi*i and so on for all branches.

Again, no! Try for example Maple (LambertW) or Mathematica (ProductLog), you can chose the branch there, for example
Code:
LambertW(-3,-Pi/2)=-2.198342630-13.98120831*I
LambertW(-2,-Pi/2)=-1.604290913-7.647192276*I
LambertW(-1,-Pi/2)=-1.570796327*I
LambertW(0,-Pi/2)=1.570796327*I
LambertW(1,-Pi/2)=-1.604290913+7.647192276*I
LambertW(2,-Pi/2)=-2.198342630+13.98120831*I
where the first argument denotes the branch.
The numbering of the branches is of course convention, but seems to match we the one given in your article (which seems to be a quite good article).
Reply


Messages In This Thread
RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by bo198214 - 11/06/2007, 01:34 PM
RE: Tetration below 1 - by Gottfried - 09/09/2007, 07:04 AM
RE: The Complex Lambert-W - by Gottfried - 09/09/2007, 04:54 PM
RE: The Complex Lambert-W - by andydude - 09/10/2007, 06:58 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  b^b^x with base 0<b<e^-e have three real fixpoints Gottfried 1 1,970 11/07/2017, 11:06 AM
Last Post: sheldonison
  2 real fixpoints again ....... tommy1729 10 8,077 02/23/2016, 10:17 PM
Last Post: tommy1729
  A new set of numbers is necessary to extend tetration to real exponents. marraco 7 8,272 03/19/2015, 10:45 PM
Last Post: marraco
  Real-analytic tetration uniqueness criterion? mike3 25 19,229 06/15/2014, 10:17 PM
Last Post: tommy1729
  About real limits tommy1729 1 2,182 09/23/2013, 09:24 PM
Last Post: tommy1729
  Solutions to f ' (x) = f(f(x)) ? tommy1729 1 2,084 08/12/2013, 12:10 AM
Last Post: tommy1729
  Real and complex behaviour of the base change function (was: The "cheta" function) bo198214 39 47,224 08/13/2011, 06:33 PM
Last Post: bo198214
  The imaginary tetration unit? ssroot of -1 JmsNxn 2 5,035 07/15/2011, 05:12 PM
Last Post: JmsNxn
  Tetration and imaginary numbers. robo37 2 5,009 07/13/2011, 03:25 PM
Last Post: robo37
  Infinite tetration of the imaginary unit GFR 40 50,321 06/26/2011, 08:06 AM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)