From: Mike Stay <metaweta@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Wednesday, July 1, 2009 3:54:09 PM Subject: Re: [math-fun] Addition formula paper Thank you, Simon, this is an interesting paper! However, it's unfortunately not the one I was looking for; also, I remember better the problem: given a function (+) of two variables x,y, find a function p() such that p(x) + p(y) = p(x (+) y) Somehow they got from x (+) y = xy to p'(x) = 1/x and then integrated to get p = log. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com _______________________________________________ Assume that p is differentiable. For the particular case, p(xy) = p(x) + p(y), we have p(1x) = p(x) + p(1), so that p(1) = 0. p(x (1 + dy)) = p(x) + p(1 + dy) p(x) + p'(x) x dy = p(x) + p(1) + p'(1) dy p'(x) = p'(1) / x -- Gene