Hi i'm new to this forum. I have a question with Laurent series.

Found below in an Eng Math text

z^2 * exp(1/z)

= z^2 * (expansion of exp(z), replacing z with 1/z )

However, as I understand eventhough exp(z) is entire (analytic

everywhere) exp(1/z) is not. so can the expansion of exp(z)

1 + z/1! + (z^2)/2! + ...

replacing z by 1/z be valid here?

thanks in advance