01/26/2011, 11:17 PM

i would like to point out :

i agree that the base change and my sinh method function are probably - without extensions - Coo but not complex analytic.

but the point is my sinh method is Coo and REAL - analytic.

Look : since log log ... exp exp ... (z) is only REAL - analytic and not complex analytic , but we can extend log log ... exp exp ... (z) simply to id(z) BECAUSE it is REAL -analytic , and then it BECOMES complex - analytic.

i agree that the base change and my sinh method function are probably - without extensions - Coo but not complex analytic.

but the point is my sinh method is Coo and REAL - analytic.

Look : since log log ... exp exp ... (z) is only REAL - analytic and not complex analytic , but we can extend log log ... exp exp ... (z) simply to id(z) BECAUSE it is REAL -analytic , and then it BECOMES complex - analytic.