• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 Differential equation for exp^[0.5] tommy1729 Ultimate Fellow     Posts: 1,370 Threads: 335 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: 1,370 Threads: 335 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^(z) - exp(z) is small ? regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Logical tetration equation Xorter 0 1,373 02/01/2018, 10:29 PM Last Post: Xorter Some sort equation ... tommy1729 0 1,603 10/15/2015, 12:12 PM Last Post: tommy1729 An intresting equation ? Taking squares by equation. tommy1729 0 1,681 05/08/2015, 11:37 PM Last Post: tommy1729 Conservation of functional equation ? tommy1729 0 1,732 05/01/2015, 10:03 PM Last Post: tommy1729 Is this THE equation for parabolic fix ? tommy1729 5 6,223 04/16/2015, 10:01 PM Last Post: tommy1729 Mick's differential equation tommy1729 3 3,323 04/10/2015, 04:14 PM Last Post: tommy1729 tommy equation tommy1729 3 4,017 03/18/2015, 08:52 AM Last Post: sheldonison Grzegorczyk hierarchy vs Iterated differential equations? MphLee 0 2,107 01/03/2015, 11:02 PM Last Post: MphLee  Inconsistant equation ? tommy1729 0 1,827 07/27/2014, 02:38 PM Last Post: tommy1729 Riemann surface equation RB ( f(z) ) = f( p(z) ) tommy1729 1 2,376 05/29/2014, 07:22 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)