Hello, I know a Taylor series for any function must be the same that laurent series of this function with a real variable, but do they have the same form always? I mean:

We know:

$\displaystyle sin x = \sum \frac{(-1)^n}{(2n+1)!} x^{2n+1}$

and:

$\displaystyle sin z =\sum \frac{(-1)^{n}}{(2n+1)!}z^{2n+1} $

If we know taylor series of f(x) and we want calculate laurent of f(z), can we just replace x for z?

Thank you.