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I am reading an old German paper, and at one step they mention that the function \begin{equation*} f(x) := \sum_{k=2}^\infty \frac{(1+x)(k(k-1)^2 + (2+x)(1+x)^2)}{(k+x)^3 (k + 1 + x)^2} \end{equation*}...

The derivatives of the function $ f(x)=x^{-x}$ have interesting properties, especially when looking at their roots. I am interested in studying the behavior of the roots of the derivatives as the ...