6. Let 0 = r R =8 and f ? H ( A (0; r, R )) . (a) Show that if f is even, then the Laurent series…

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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.