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![\color{blue}\text{ if }\Re[z]<0\text{ and }0<a\leq 1,](http://www.mathhelpforum.com/math-help/latex2/img/7997c8ff6f2bb4fa80412931e6ab2f1f-1.gif "\color{blue}\text{ if }\Re[z]<0\text{ and }0<a\leq 1,")
![\color{blue}\zeta(z,a)=\frac{2\Gamma(1-z)}{(2\pi)^{1-z}}\left[\sin\left(\frac{\pi z}{2}\right)\sum_{n=1}^{\infty}\frac{\cos(2\pi a n)}{n^{1-z}}+\cos\left(\frac{\pi z}{2}\right)\sum_{n=1}^{\infty}\frac{\sin(2\pi a n)}{n^{1-z}}\right]](http://www.mathhelpforum.com/math-help/latex2/img/2a5294e653c20ce63d99502635321876-1.gif "\color{blue}\zeta(z,a)=\frac{2\Gamma(1-z)}{(2\pi)^{1-z}}\left[\sin\left(\frac{\pi z}{2}\right)\sum_{n=1}^{\infty}\frac{\cos(2\pi a n)}{n^{1-z}}+\cos\left(\frac{\pi z}{2}\right)\sum_{n=1}^{\infty}\frac{\sin(2\pi a n)}{n^{1-z}}\right]")
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