07/18/2008, 01:48 PM

martin Wrote:Oy, I'm not so good at explaining things, but I'll try anyway.

and exercise makes you better and better

Quote:all the "common" mean values (arithmetic, geometric, quadratic and harmonic mean) can be expressed in the form [(a(1)^n+a(2)^n+...+a(m)^n)/m]^(1/n). For n=1, this is the arithmetic mean, for n=2 the quadratic, for n=-1 the harmonic, and, by analytic continuation or whatever you may call it, for n=0 the geometric mean.

Thats interesting! Can you give a proof for n=0, i.e that

?

Quote: I assumed that, with such a flexible mean value calculation, it just had to work. All I had to do was figure out the appropriate parameter n for a given interval [x ... x+1]. But lately I started doubting this assumption as well.

So the formula is the generalized mean of what? *headscratch*