First i turned cos(2z)=e2iz+e−2iz2, then using the taylor series of ezI calculated the taylor series of both arguments.
e2iz2=∞∑n=0(i)n2n−1znn!
e−2iz2=∞∑n=0(−i)n2n−1znn!
From this stage i dont know how to continue.
Is my way to the solution is right?
Answer
Hint:
(i)n+(−i)n=einπ2+e−inπ2=2cosnπ2.
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