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+--- Thread: Differential equation for exp^[0.5] (/showthread.php?tid=903)
Differential equation for exp^[0.5] - tommy1729 - 07/14/2014
We know the logarithmic derivative is f ' / f dz.
We know the solve derivative is dz / ( f ' (inv f) ).
Let f = exp^[0.5].
Then solve f = inv f = ln(f).
THUS f ' / f = 1 / ( f ' (ln(f)) )
I wonder how good approximations of f satisfy the differential equation. (2sinh , base change , fake etc )
What about theta(z) ??
regards
tommy1729
RE: Differential equation for exp^[0.5] - tommy1729 - 07/26/2014
(07/14/2014, 12:55 AM)tommy1729 Wrote: We know the logarithmic derivative is f ' / f dz.
We know the solve derivative is dz / ( f ' (inv f) ).
Let f = exp^[0.5].
Then solve f = inv f = ln(f).
THUS f ' / f = 1 / ( f ' (ln(f)) )
I wonder how good approximations of f satisfy the differential equation. (2sinh , base change , fake etc )
What about theta(z) ??
regards
tommy1729
I wonder if g ' / g = 1 / (g ' (h(g)))
where h is a fake ln would make a good fake g(z) such that g^[2](z) - exp(z) is small ?
regards
tommy1729