Define a Leibniz series as follows, \begin{eqnarray*} L(x) & = & \sum_{k=1}^{\infty}(-1)^{k}e^{-kx}\ln k,\ \ x>0 \end{eqnarray*}

I have two questions: (I) Is there an analytical form for $L(x)$? (II) Does the analytic continuation for $L(x)$ from region $x>0$ to region $x<0$ exist?

  • $\begingroup$ Do you have motivations for this problem? What have you tried? $\endgroup$ Sep 22, 2016 at 13:14


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