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Just asking...
#5
Sorry, I thought you already considered this type of formula or made a quick check about derivatives and such ... anyway, my "function" here is continuous and differentiable (as far as I understand what that means), but not infinitely often differentiable. The 3rd derivative has a slight peak near the integer points that I didn't manage to wipe away with a higher accuracy of my "parameter" 0.345627(2-x), or maybe Excel is just too inaccurate there. I've tried similar formulae before, but never got this close (e.g. had this peak already in the 2nd derivative).

Generally, for a better understanding, I was originally searching a function between x and x+1, such that log(f(x))/log(b) below x and b^f(x) above x+1 runs smoothly together to a continuous, monotonously increasing line on a graph. (I could explain more details, if you care to hear the whole story.)

I had in mind that this might be a formula, even if it only gives approximated values, that is not too complicated to calculate with. (Okay, I still would need to find a way to get a general formula to substitute this 0.345627-thingy for other bases.) Or, if there is a way to get that peak out of the 3rd derivative and eventually make it infinitely differentiable, whether the results are congruent to already existing results or they aren't.
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Messages In This Thread
Just asking... - by martin - 07/14/2008, 09:49 PM
RE: Just asking... - by bo198214 - 07/14/2008, 10:53 PM
RE: Just asking... - by martin - 07/15/2008, 11:40 AM
RE: Just asking... - by bo198214 - 07/16/2008, 08:00 PM
RE: Just asking... - by martin - 07/16/2008, 09:52 PM
RE: Just asking... - by bo198214 - 07/16/2008, 10:36 PM
RE: Just asking... - by bo198214 - 07/16/2008, 10:52 PM
RE: Just asking... - by martin - 07/17/2008, 11:28 AM
RE: Just asking... - by bo198214 - 07/18/2008, 01:48 PM
RE: Just asking... - by martin - 07/18/2008, 06:37 PM
RE: Just asking... - by bo198214 - 07/18/2008, 10:02 PM
RE: Just asking... - by Gottfried - 07/19/2008, 03:48 AM
RE: Just asking... - by Ivars - 07/19/2008, 07:04 AM
RE: Just asking... - by martin - 07/19/2008, 09:03 AM
RE: Just asking... - by Ivars - 07/19/2008, 07:45 PM
RE: Just asking... - by andydude - 07/21/2008, 04:05 AM
RE: Just asking... - by martin - 07/21/2008, 06:31 PM
RE: Just asking... - by Ivars - 07/22/2008, 06:07 AM



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