It has puzzled me for a long time that **the Feigenbaum constant $\delta$ and reduction parameter $\alpha$ do not seem to be related to other constants** (that is, numerically), even not to each other. In fact I have never seen them expressed as an integral, any kind of series or product, a nested expression, ... The only thing I have found on the internet is [this algorithmic approach][1] which further links to [this][2], but it seems rather like an "a posteriori" method, being interested more in the algorithm than in the nature of $\delta$. Moreover, it was written several years ago.

On the other hand, I wouldn't be *too* surprised to see $\delta$ written as a continued fraction, given the fact that it can be defined by 
$\delta=\lim\limits_{n\to\infty}\dfrac{\mu_n-\mu_{n-1}}{\mu_{n+1}-\mu_n}$, where the $\mu_n$ are the bifurcation points of an iterated map. But I have never seen one either. Any leads?


  [1]: http://marvin.sn.schule.de/~inftreff/modul48/modul48.htm
  [2]: http://marvin.sn.schule.de/~inftreff/modul24/task24.htm