Generalized recursive operators

[Ivars]

You're right, I'm wrong. \( \lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = -1.85 \) not -2 as I had first thought. Jay has found the more precise values in this thread which you should look to instead of this post, as I'm only accurate to 1 decimal place.

Andrew Robbins

So what are the exact values for :

\( \lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 7 \\\hline\end{tabular} b) = ? \)

\( \lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 9\\\hline\end{tabular} b) = ? \)

\( \lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 11\\\hline\end{tabular} b) = ? \)

etc?

I am looking for them to prove or disprove the fine structure constant approximation which seems to improve with each next value above [5], but the accuracy is bad as I took them from Andrew's graph.

Thank You in advance,

Ivars