May be a stupid question:
1) For domain x<e^-e can odd and even h(x) be looked upon as separate continuous or infinitely differentiable functions?
2) Would the same apply to superroots in their oscillating domain?
3) If we denote them h odd(x) , h even (x) , can we make a function:
f(x) = h odd (x) / h even (x)? or h even (x) * h odd (x)? And perhaps similar one for supperroots?
4) what will happen with that function h odd(x)/h even(x) at x=0
And what will happen with h even (x) * h odd (x) at point x=0?
The values will be 0, but how can it be?
5) If we could than divide
h odd (x)/h even(x) at x=0 which is 0 with
h even (x) * h odd (x) at x=0 which is 0 again then we have
(h odd (0) /h even (0) ) / ((h even (0) * h odd (0)) = 1/h^2 even(0) = 1/1= (0/0)
If we do it other way around, we get h^2 even (0)/1 = 1/1= 0/0
For superroots, it will be odd function squared that will lead to 0/0. Obviosly that seems not to be true, since 0/0 is undefined, so we need to differentiate away the 0-es but it seems to me we can not do it even by infinite application of lHopitals rule.
I have a feeling that somehow we need an extra dimension to resolve this. But may be this is just another miss
Excuse me.
Ivars
1) For domain x<e^-e can odd and even h(x) be looked upon as separate continuous or infinitely differentiable functions?
2) Would the same apply to superroots in their oscillating domain?
3) If we denote them h odd(x) , h even (x) , can we make a function:
f(x) = h odd (x) / h even (x)? or h even (x) * h odd (x)? And perhaps similar one for supperroots?
4) what will happen with that function h odd(x)/h even(x) at x=0
And what will happen with h even (x) * h odd (x) at point x=0?
The values will be 0, but how can it be?
5) If we could than divide
h odd (x)/h even(x) at x=0 which is 0 with
h even (x) * h odd (x) at x=0 which is 0 again then we have
(h odd (0) /h even (0) ) / ((h even (0) * h odd (0)) = 1/h^2 even(0) = 1/1= (0/0)
If we do it other way around, we get h^2 even (0)/1 = 1/1= 0/0
For superroots, it will be odd function squared that will lead to 0/0. Obviosly that seems not to be true, since 0/0 is undefined, so we need to differentiate away the 0-es but it seems to me we can not do it even by infinite application of lHopitals rule.
I have a feeling that somehow we need an extra dimension to resolve this. But may be this is just another miss
Excuse me.
Ivars