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 Just asking... martin Junior Fellow  Posts: 14 Threads: 1 Joined: Jul 2008 07/17/2008, 11:28 AM Oy, I'm not so good at explaining things, but I'll try anyway. When I first tried to interpolate b^^x for non-integer x (and for easy cases like 2^^x or 3^^x), I thought of the following: For example, 3^^0=1, 3^^1=3, 3^^2=27 - at first, the values appear to grow linearly, then exponentially. So I came up with the idea of a "flexible arithmetic-geometric mean". I expected the function to grow like a linear function ax+b at one point x and like a geometric series a^x*b at x+1, but that didn't turn out to be the case. That was about three years ago. Playing around with numbers and maths in general being my hobby, I hit upon the following last year: 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. 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. Darn, now I begin to see what you meant ... if this formula works between x and x+1, why shouldn't it also work beyond this interval? Seems I'm being still too much of an amateur here. bo198214 Wrote:Polynomials are not complicated to calculate with either, are they? Polynomials are not bad, really. I'm just not familiar with making polynomials with degree >= 2 out of given values. « Next Oldest | Next Newest » 