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