Hmm, perhaps I have made some basic error now, or something is around which I did not understand correctly from the beginning.
It is clear, that the \( \operatorname{asum}(x) \) is 2-periodic, that means \( \operatorname{asum}(x_{-1})=\operatorname{asum}(x)=\operatorname{asum}(x_1)=... \)
The same seems obvious to me for the asum-derivatives in that periods. But I get different values for the first and second derivatives when I simply shift the center by 2 iterations. Here is a numerical protocol, where I use x1=3.2 (just a random value), and then compute the zero'th, first and second derivative:
Can someone crosscheck and possibly explain that? Or do I have only a knot in my head?
Well I asked that question also in MSE, and it might be a bit more instructive. Possibly I'm beginning to understand - but still not getting it in all of its consequences. I'll continue this observation/thoughts here later again... See the question in MSE
http://math.stackexchange.com/questions/...d-infinite
Hmm, after some hours thinking about it becomes a bit similar to the situation, when a little kitten finds its own tail first time and begins to run after it in circles... :-) Obviously I must have the answer for this already in my own analytic formulae for the evaluation of the asum and its derivatives
Gottfried
It is clear, that the \( \operatorname{asum}(x) \) is 2-periodic, that means \( \operatorname{asum}(x_{-1})=\operatorname{asum}(x)=\operatorname{asum}(x_1)=... \)
The same seems obvious to me for the asum-derivatives in that periods. But I get different values for the first and second derivatives when I simply shift the center by 2 iterations. Here is a numerical protocol, where I use x1=3.2 (just a random value), and then compute the zero'th, first and second derivative:
Code:
. [ x2=exph(x1,0), asum(x2), asum_deriv(x2,1), asum_deriv(x2,2)]
%697 = [3.20000000000, -0.00119822450167, 0.0175377529574, 0.000817628416425]
[ x2=exph(x1,2), asum(x2), asum_deriv(x2,1), asum_deriv(x2,2)]
%698 = [0.412136407584, -0.00119822450167, 0.0779236358328, -0.129878114856]Can someone crosscheck and possibly explain that? Or do I have only a knot in my head?
Well I asked that question also in MSE, and it might be a bit more instructive. Possibly I'm beginning to understand - but still not getting it in all of its consequences. I'll continue this observation/thoughts here later again... See the question in MSE
http://math.stackexchange.com/questions/...d-infinite
Hmm, after some hours thinking about it becomes a bit similar to the situation, when a little kitten finds its own tail first time and begins to run after it in circles... :-) Obviously I must have the answer for this already in my own analytic formulae for the evaluation of the asum and its derivatives
Gottfried
Gottfried Helms, Kassel
