Solve, in Complex Variable Function and Laplace Transform, why can the expansion of Laurent series be directly expanded by ready-made Taylor series? They are in two grades.

No strict proof, just personal feelings,

Laurent series should aim at analyzable functions.

Analytic complex function is very similar to real function, for example, the derivative and formula are exactly the same, and the derivative f'(z) of f(z) is the same whether z is a complex number or a real number.

Based on this similarity or symmetry. . .

The series will have the same form.

I don't study pure mathematics either. It is very likely that what I said is unscientific, which is my personal opinion.