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 Half-iteration of x^(n^2) + 1 tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 02/13/2017, 12:12 PM I was intrested in the half-iteration of f_n(x) = x^(n^2) + 1 for Large x. For instance g_n(x) = f_n ^[1/2](x) - x^n. H_n(x) = f_n ^[1/2](x) / x^n. For Large x : Is abs g_n(x) increasing or decreasing with n ? Is abs H_n(x) decreasing ? Probably abs g_n is increasing and abs H_n decreasing. The focus is on integer n and branch structure. But also if n is real , are these functions analytic in n ? Perturbation Theory suggests this. I wonder how these functions look like on the complex plane , especially with resp to n. Regards Tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Half-iteration of x^(n^2) + 1 - by tommy1729 - 02/13/2017, 12:12 PM RE: Half-iteration of x^(n^2) + 1 - by Xorter - 03/04/2017, 11:43 AM RE: Half-iteration of x^(n^2) + 1 - by tommy1729 - 03/09/2017, 01:28 PM RE: Half-iteration of x^(n^2) + 1 - by Xorter - 03/09/2017, 10:02 PM

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