11/21/2007, 07:51 AM

Gottfried Wrote:I get for the sum of both by my matrix-method

Code:`.`

Sb(x) + Rb(x) = V(x)~ *Mb[,1] + V(x)~ * Lb[,1]

= V(x)~ * (Mb + Lb)[,1]

= V(x)~ * I [,1]

= V(x)~ * [0,1,0,0,...]~

= x

Sb(x) + Rb(x) = x

This is what I have the most trouble understanding. First what is your [,1] notation mean? I understand "~" is transpose, and that Bb is the Bell matrix . Second, what I can't see, or is not obvious to me at least, is why:

Is there any reason why this should be so? Can this be proven?

Wait, I just implemented it in Mathematica, and you're right! (as right as can be without a complete proof). Cool! This may just be the single most bizarre theorem in the theory of tetration and/or divergent series.

Andrew Robbins