Question

Difference between analytic and holomorphic function

Answer 1

For complex functions they are equivalent, but not by definition the same.

For a function to be analytic in a point, it needs  to have a powerseries expansion around that point.

For a function to be holomorphic in a point, it needs to be complex differentiable in that point.

You can prove that the two conditions are equivalent for functions on the complex plane.