Following are two examples on one way of finding Laurent series using Maple.

Give two different functions and find their Laurent series.

Finding the Laurent series of  .

> f:='f': z:='z':

f := z ->(cos(z) - 1)/z^4:

`f(z) ` = f(z);

> L:='L': s:='s': S:='S': Z:='Z':

S := series(cos(Z)-1, Z=0, 8)/Z^4:

s := convert(series(cos(Z)-1, Z=0, 8), polynom)/Z^4:

LS := z -> subs(Z=z,expand(s)):

`f(z) ` = f(z);

`f(z) ` = subs(Z=z,S);

`f(z) ` = series((cos(z) - 1)/z^4, z=0, 8);

Finding the Laurent series of  .

> f := 'f': S:='S': z:='z':

f := z -> exp(-1/z):

S := series(f(z), z=infinity, 10):

`f(z) ` = f(z);

`f(z) ` = S;