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 Half-iteration of x^(n^2) + 1 Xorter Fellow Posts: 93 Threads: 30 Joined: Aug 2016 03/09/2017, 10:02 PM (03/09/2017, 01:28 PM)tommy1729 Wrote: Thank u for your reply. However i have questions 1) your coëfficiënt 1/2048 occurs twice !? Are you sure about that. 2) also the coëfficiënts : i noticed all of them ( though truncated ) are positive. Does this pattern remain ? Are they correct ? 3) not sure how you computed it. I assume no fixpoint but a kind of carleman matrix method ? If you used a fixpoint , which one ? 4) im intrested in using the fix with largest real part. Regards Tommy1729. I did not use fixpoint, because by the Carleman matrix it can be calculated, too. You can see above, how I computed. Just save it in gp and open it with gp.exe and enter this code: Decar(Msqrt(Car(x^4+1,20),20,5),20)*1.0 Where Car makes a 20x20 Carleman matrix from x^4+1, Msqrt get its square root and Decar gets the Taylor series of the function from the matrix. It is simple, because: M[f]M[g]=M[fog] thus sqrt M[f] = M[f^o0.5], right? Of course! N root of M[f] = M[f^o1÷N] If you check the code above, you can see it has a lot of (infinity) part with negative sign. Naturally, it is not perfect, the bigger Carleman matrices you use, the better the results are. Xorter Unizo « 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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