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Regarding the expression of $f(1)$ in terms of other known constants: $$f(1) = -e\left(\gamma + \sum_{n\geq 1} (-1)^n \frac1{n\cdot n!} \right) \qquad\quad \tag{$*$} \label{id}$$ $$\qquad\qquad\qquad= -e \left(\gamma - 1 + \frac1{4} - \frac1{18} + \frac1{96} - \frac1{600} + \cdots \right)$$ where $e = \sum_{n\geq0} \frac1{n!} \approx 2.718$ and $\gamma \...


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