Question

Obtain the Taylor series expansion of cos^2zabout z = 0.

Answer 1

Answer on Question #85331 - Math - Complex Analysis

$$\cos^2(\mathbf{z}) = \frac{1 + \cos(2\mathbf{z})}{2} = \frac{1 + \sum_{n=0}^{\infty} (-1)^n \frac{(2\mathbf{z})^2n}{(2n)!}}{2} = 1 + \sum_{n=1}^{\infty} (-1)^n \frac{2^{2n-1}}{(2n)!} \mathbf{z}^{2n}$$

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