fake id(x) for better 2sinh method.

[tommy1729]

There is a problem with this particular type of fake function.
Although it may be fixed as stated in post 1 it seems a big problem.

Perhaps the biggest problem of " fake function theory ".

id(x) as desired in post nr 1 : " fake id(x) behaves like e/2 x for small x, like x for large real and like 0 for large imaginary part "

is in contradiction with the well known Lindelöf theorem.

It seems the natural fix is : " fake id(z) behaves like e/2 z for small z and like z for large z "

regards

tommy1729