• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 [2014] tommy's theorem sexp ' (z) =/= 0 ? tommy1729 Ultimate Fellow Posts: 1,454 Threads: 350 Joined: Feb 2009 06/17/2014, 12:18 PM Let sexp(z) be a solution that is analytic in the entire complex plane apart from z=-2,-3,-4,... if w is a (finite) nonreal complex number such that sexp ' (w) = 0 then it follows that for real k>0 : sexp ' (w+k) = 0. Proof : chain rule exp^[k] is analytic : sexp(w+k) = exp^[k](sexp(w)) sexp ' (w+k) = exp^[k] ' (sexp(w)) * sexp ' (w) = 0 Hence we get a contradiction : sexp is not nonpolynomial analytic near w (or w + k). Conclusion there is no w such that sexp'(w) = 0. Consequences : since 0 < sexp ' (z) < oo slog ' (z) is also 0 < slog ' (z) < oo since exp^[k](v) = sexp(slog(v)+k) D exp^[k](v) = sexp ' (slog(v)+k) * slog ' (v) = nonzero * nonzero = nonzero.. => 0 < exp^[k] ' (z) < oo Tommy's theorem Strongly related to the TPID 4 thread and some recent conjectures of sheldon. the analogue difference is not understood yet. (posted that already) regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread [2014] tommy's theorem sexp ' (z) =/= 0 ? - by tommy1729 - 06/17/2014, 12:18 PM RE: [2014] tommy's theorem sexp ' (z) =/= 0 ? - by sheldonison - 06/17/2014, 01:25 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Tommy's Gaussian method. tommy1729 16 274 59 minutes ago Last Post: JmsNxn Some "Theorem" on the generalized superfunction Leo.W 29 2,777 06/25/2021, 09:42 PM Last Post: Leo.W " tommy quaternion " tommy1729 13 3,054 03/23/2021, 01:21 PM Last Post: tommy1729 tommy's simple solution ln^[n](2sinh^[n+x](z)) tommy1729 1 4,598 01/17/2017, 07:21 AM Last Post: sheldonison Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) tommy1729 0 2,934 09/06/2016, 04:23 PM Last Post: tommy1729 Tommy's matrix method for superlogarithm. tommy1729 0 3,037 05/07/2016, 12:28 PM Last Post: tommy1729 Dangerous limits ... Tommy's limit paradox tommy1729 0 3,188 11/27/2015, 12:36 AM Last Post: tommy1729 Tommy's Gamma trick ? tommy1729 7 11,273 11/07/2015, 01:02 PM Last Post: tommy1729 Tommy triangles tommy1729 1 3,694 11/04/2015, 01:17 PM Last Post: tommy1729 Tommy-Gottfried divisions. tommy1729 0 2,819 10/09/2015, 07:39 AM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)