6. Let 0 ≤ r R ≤∞ and f ∈ H(A(0; r, R)). (a) Show that if f is even, then the Laurent series of f on A(0; r, R) has nonzero terms only of even degree. (b) Show that if f is odd, then the Laurent...

6. Let 0
≤

r



R

≤∞

and
f

∈

H(A(0;
r,


R)).

(a) Show that if
f
is even, then the Laurent series of
f
on
A(0;
r,


R) has nonzero terms only of even degree.

(b) Show that if
f
is odd, then the Laurent series of
f
on
A(0;
r,


R) has nonzero terms only of odd degree.