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 Differential equation for exp^[0.5] tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 07/14/2014, 12:55 AM 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 tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 07/26/2014, 12:27 PM (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 « Next Oldest | Next Newest »

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