tommy's simple solution ln^[n](2sinh^[n+x](z)) tommy1729 Ultimate Fellow Posts: 1,859 Threads: 402 Joined: Feb 2009 01/16/2017, 01:29 PM Consider f(z,x) = Lim(n --> oo)  ln^[n] ( 2sinh^[n+x] (z) ). This simple Function satisfies exp(f(z,x)) = f(z,x+1). So we have a simple superfunction that requires only the real iterations of 2sinh(z). Notice lim ( n --> oo) 2sinh^[n]( 2^(z-n)) is a superf for 2sinh. f(z,x) could be analytic for re(z) > 1. Also , is it really new ? Or is it the ( analytic continuation ? ) of the 2sinh method ? It sure is very similar. ---- Mick wondered if F^[n] ( g^[n] ) is analytic for f = sqrt and g = x^2 +1. --- Regards Tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread tommy's simple solution ln^[n](2sinh^[n+x](z)) - by tommy1729 - 01/16/2017, 01:29 PM RE: tommy's simple solution ln^[n](2sinh^[n+x](z)) - by sheldonison - 01/17/2017, 07:21 AM

 Possibly Related Threads… Thread Author Replies Views Last Post [MSE too] more thoughts on 2sinh tommy1729 1 73 02/26/2023, 08:49 PM Last Post: tommy1729 [NT] Caleb stuff , mick's MSE and tommy's diary functions tommy1729 0 59 02/26/2023, 08:37 PM Last Post: tommy1729 " tommy quaternion " tommy1729 37 11,357 02/14/2023, 11:47 PM Last Post: tommy1729 tommy's "linear" summability method tommy1729 15 504 02/10/2023, 03:55 AM Last Post: JmsNxn Maybe the solution at z=0 to f(f(z))=-z+z^2 Leo.W 9 328 01/24/2023, 12:37 AM Last Post: tommy1729 Semi-group iso , tommy's limit fix method and alternative limit for 2sinh method tommy1729 1 240 12/30/2022, 11:27 PM Last Post: tommy1729 tommy's group addition isomo conjecture tommy1729 1 367 09/16/2022, 12:25 PM Last Post: tommy1729 tommy's displacement equation tommy1729 1 368 09/16/2022, 12:24 PM Last Post: tommy1729 semi-group homomorphism and tommy's U-tetration tommy1729 5 692 08/12/2022, 08:14 PM Last Post: tommy1729 The Etas and Euler Numbers of the 2Sinh Method Catullus 2 556 07/18/2022, 10:01 AM Last Post: Catullus

Users browsing this thread: 1 Guest(s)