GFR Wrote:\( \lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = -1.85.. \), and:
\( \lim_{b\rightarrow-1.85..}(e \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = -\infty \)
Wah, the second one is wrong! As Andydude wrote, the odd hyperexponentials are bounded below. The even hyper exponentials b[2n]x are not bounded below but only defined on -2n+2=-(2n-3)-1<x.
We have the general relation
\( \lim_{x\to -2n+2} \) b[2n]x = \( -\infty \).
in this case:
\( \lim_{x\to -4} \) b[6]x = \( -\infty \)
though that is probably not right either. But the true value \( -2n+2<X<-2n+3 \)
\( \lim_{x\to X} \) b[2n]x = \( -\infty \).