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 zero's of exp^[1/2](x) ? tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 12/29/2015, 01:23 PM (12/08/2010, 02:24 PM)sheldonison Wrote: (12/08/2010, 01:39 PM)tommy1729 Wrote: then sexp(-3.5) , sexp(-4.5) , ... sexp(-(2n+1)/2) should all have a singularity because sexp(x-1) = ln(sexp(x)) right ?yes, but I don't know where they would be in the complex plane. sexp(-2.5)=-0.36237+iPi, and if you follow a path from -0.36237 to -0.36237+iPi, the singularity is right there (plotted the path earlier). But, for sexp(-3.5) = 1.1513+i1.6856, I'm not sure what the path would be in the complex plane. If I naively calculate slog(1.1513+i1.6856), I get 0.94439+i1.12428, which has no connection to the predicted singularity at exp^[0.5](sexp(-3.5)). - Sheldon I conjecture that - using mike3 branches - L and L* are the only singularities. Also i think 0.94 + 1.12 i is a singularity but on a nearby branch. Mike3 branches match very Well with the fake exp^[1/2]. So im intrested in the other branches ( and pics ) and also their fake analogues - although that fake should Maybe be discussed in another thread. I think it is justitied to search the sigularities by starting from re part and then going Up or down the branches. ( like sheldon did in part ) For negative real parts there are 3 lines to start with - using mike3 branches - , not sure how to decide. That's alot of " new " conjectures , although i had them for years actually. Just decided to post them now. Recently ( dec 2015 ) Sheldon started a thread about the singularity at L. I will only talk about that there. I wish you all a good 2016. Regards Tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread zero's of exp^[1/2](x) ? - by tommy1729 - 12/04/2010, 12:16 AM RE: zero's of exp^[1/2](x) ? - by JJacquelin - 12/07/2010, 08:53 AM RE: zero's of exp^[1/2](x) ? - by sheldonison - 12/07/2010, 01:03 PM RE: zero's of exp^[1/2](x) ? - by mike3 - 12/08/2010, 02:44 AM RE: zero's of exp^[1/2](x) ? - by sheldonison - 12/08/2010, 10:16 AM RE: zero's of exp^[1/2](x) ? - by tommy1729 - 12/08/2010, 01:03 PM RE: zero's of exp^[1/2](x) ? - by sheldonison - 12/08/2010, 01:09 PM RE: zero's of exp^[1/2](x) ? - by tommy1729 - 12/08/2010, 01:39 PM RE: zero's of exp^[1/2](x) ? - by sheldonison - 12/08/2010, 02:24 PM RE: zero's of exp^[1/2](x) ? - by tommy1729 - 12/29/2015, 01:23 PM mild singularity at L, RE: zero's of exp^[1/2](x) ? - by sheldonison - 12/10/2010, 08:35 PM RE: mild singularity at L, zero's of exp^[1/2](x) ? - by mike3 - 12/11/2010, 09:21 AM RE: zero's of exp^[1/2](x) ? - by tommy1729 - 12/08/2010, 12:32 AM singularities and zero's of (2*sinh)^[1/2](z) ? - by tommy1729 - 02/17/2011, 11:56 PM RE: zero's of exp^[1/2](x) ? - by tommy1729 - 11/14/2012, 05:11 PM

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