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András Bátkai
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Closed form expression for this infinite series?

Is there a closed-form expression for this series?

$\displaystyle\sum_{k\geq 1}^\infty \frac{\lambda^k e^{-\lambda}}{k!}\cdot[1-(1-x)^k]\cdot \frac{1}{k}$

Any answers, ideas or references would be appreciated.

John
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