Let r be a real number.
^[r] is the r-th iteration. hence exp^[r] is tetration with base e.
a [r] b = b [r] a = exp^[r]( exp^[-r](a) + exp^[-r](b) )
now the extended distributive property is
a [r] ( b [r-1] c ) = ( a [r] b ) [r-1] ( a [r] c )
and once again tetration plays an underestimated important role.
Below is a link to my profile at the tetration forum.
At the moment I only accept the tetration forum as a good source for tetration although you can find some info and links on wiki , I do however not accept the wiki page.
Thank you for your intrest.