Derivatives on HP 42S

[Albert Chan]

(08-25-2018 08:00 PM)Thomas Klemm Wrote:  

(08-25-2018 07:03 PM)Albert Chan Wrote:  If x < 0 and y is odd integer, return -(-x) ^ (1/y), else x ^ (1/y)

Unfortunately \(x=\Re[z]\) and \(y=\Im[z]\) aren't analytic functions.
So anything based on these values isn't analytic as well.

Can you explain the word analytic ?
Is this the cost of using complex numbers ? (even using the real part not allowed ?)

Is f(x) = x^(1/3) an analytic function ?
If x is complex, is it true that f(x) same as -f(-x) ?

Googling "function not analytical":

A complex function is said to be analytic on a region if it is complex differentiable at every point in.
The terms holomorphic function, differentiable function, and complex differentiable function are
sometimes used interchangeably with "analytic function" (Krantz 1999, p. 16).

After above googling, click the graph, you get wikipedia explanation:

non-analytic smooth function is a smooth function which is nowhere real analytic