Complex Series

**joshquick** · December 8th 2010, 12:04 AM

Show that

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

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!

**FernandoRevilla** · December 8th 2010, 12:40 AM

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

Demostraciones Matematicas problemas ejercicios preguntas consultas dudas ayuda apoyo, tareas. Foros. Tex, Latex Editor. Latexrender. Math help

Regards.

Fernando Revilla

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

Thread: Complex Series

LinkBack

Thread Tools

Display

Complex Series

Similar Math Help Forum Discussions

Complex series

Complex Series

Complex Power Series

Sum of complex series

Complex Series

Search Tags