# Math Help - Complex Series

1. ## Complex Series

Show that

$\frac{\pi}{\cos(\pi z)} = 4\sum_{n=0}^{\infty} \frac{(-1)^n (2n+1)}{(2n+1)^2 - 4z^2}
$

So if you see my attempt here at first working around the tangent function decomposition [link], and making use of the identities $\cot(\pi z) + \tan(\frac{\pi}{2}z) = \frac{1}{\sin(z)}$, and $\cos(\pi z) = \sin(\pi(\frac{1}{2} - z))$, I haven't been going anywhere with this.

Appreciate any help. Thank you!

2. You can use the Mitagg_Leffler theorem. Here, I solve $f(z)=1/\cos z=\ldots$

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Regards.

Fernando Revilla

P.S. It is in Spanish. If necessary, I can translate it.