The function #y = x^x# is differentiable at x = 1/e, What is the Taylor series ( if any ) for y, about x = 1/e?
At x = 1/e, y =
It is easy to prove that the derivatives of all orders vanish at x = 1/e.
So, the function should behave as
in an infinitesimal neighborhood
The graph of
contact, with the bracing tangent
In my opinion, this contact is transcendental..