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Math Help - Complex Series

  1. #1
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    Complex Series

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    \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!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    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.
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