Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 05/09/2008, 06:32 AM Hi experts, Please tell me what are the exact values of selfzeros on the outer shape for b= 3/2, 2, sqrt(3) , 3, 4? (it is +-I for b= e^(pi/2))? Thank You in advance, Ivars Gottfried Ultimate Fellow Posts: 898 Threads: 130 Joined: Aug 2007 03/03/2011, 03:16 PM While the solution of the problem to find complex fixpoints t for real bases b>exp(exp(-1)) using Lambert-W which were given here satisfies all needs the problem was only unsatisfactory solved for the case of numerical evaluation when the Lambert-W including the choice of branches is not available in a software (like Pari/GP). My own proposal was based on a binary search using a formula depending on a single parameter beta. But because the number of iterations for good approximations increase quickly I tried to improve that method by employing Newton/Raphson instead of binary search. That led to a solution where I need only 10 to 15 iterations (number of correct digits seem to increase quadratically), and also gave an interesting powerseries for the involved function which must iterated. Here is the link to my treatize in the discussion platform math.stackexchange: http://math.stackexchange.com/questions/...t-function Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post Range of complex tetration as real Daniel 2 464 10/22/2022, 08:08 PM Last Post: Shanghai46 From complex to real tetration Daniel 3 506 10/21/2022, 07:55 PM Last Post: Daniel Cost of real tetration Daniel 1 406 09/30/2022, 04:41 PM Last Post: bo198214 Real Multivalued/Parametrized Iteration Groups bo198214 11 1,339 09/10/2022, 11:56 AM Last Post: tommy1729 Constructive real tetration Daniel 1 404 09/01/2022, 05:41 AM Last Post: JmsNxn Real and complex tetration Daniel 1 495 08/17/2022, 01:56 AM Last Post: JmsNxn Complex to real tetration Daniel 1 413 08/14/2022, 04:18 AM Last Post: JmsNxn Constructing a real valued Fibonacci iteration--its relation to $$1/1+z$$ JmsNxn 7 828 08/13/2022, 12:05 AM Last Post: JmsNxn Convergent Complex Tetration Bases With the Most and Least Imaginary Parts Catullus 0 418 07/10/2022, 06:22 AM Last Post: Catullus Challenging the concept of real tetration Daniel 2 596 07/04/2022, 03:09 PM Last Post: Daniel

Users browsing this thread: 1 Guest(s)