02/24/2009, 09:57 PM

sheldonison Wrote:

A very appealing formula (though the two limits belong to the right side of the equal sign)!

For my taste, if I rewrite and generalize your formula a bit ad hoc (dont know whether it is true in that form):

has a big similarity to Zdun's [1] formula for regular iteration (where is assumed to have fixed point at 0):

, .

Only is replaced by . But be aware that , which makes the similarity even more striking.

[1] Zdun, Marek Cezary. Regular fractional iterations. Aequationes Math. 28 (1985), no. 1-2, 73--79. MR0781210