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Also for the Liouville function we have
: <math> \sum_{n=1}^\infty \frac{\lambda(n)}{\sqrt{n}}g(\log n) = \sum_{\rho}\frac{h( \gamma)\zeta(2 \rho )}{\zeta'( \rho)} + \frac{1}{2\zeta (1/2)}\int_{-\infty}^\infty dx \, g(x) .</math>
For the Euler-Phi function the explicit formula reads
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