Seem to remember reading about RF experimenting with non-integer differentiation. I found it quite interesting to play with. I started with 'half' differentiation. e.g. f(x) = x^2 , Df = 2x , Df = 2 but what about non-integer diff? e.g. D[0.5]f = px^1.5 what is p? Clearly D[0.5]D[0.5]f = Df and D(x^n) = nx^n-1 So D[0.5](x^n) = p(n)x^(n-0.5) and D[0.5]( p(n)x^(n-0.5) ) = p(n)p(n-0.5)x^(n-1) which is equal to D(x^n) = nx^(n-1) so p(n)p(n-0.5) = n From this I figure the key to finding p is solving the formula... p(n)*p(n-0.5) = n . It looks abit like the gamma function G(n+1)/G(n) = n and considering the solution to the gamma function, I decide that solving my non-integer diff formula is beyond me. I've got a pretty good approximation though. p ~= ((x+0.5)^0.5 + x^0.5)/2 for x>1 hmm. Is this 'genaralized' diff alreadly established math? Since calculus is so central to math,it seems to me that any generalization has broad applications.