• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 some questions about sexp tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 06/28/2010, 11:18 PM im going to ask some questions about sexp , and i mean all proposed solutions of sexp. (question 1) does the following hold : d f^n / d x^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k ? (question 2) since slog(z) (base e) has period 2pi i why doesnt sexp(z) look like a log spiral ? or does it , like having a branch cut at real x < -2 ? (question 3) what happens to limit cycles and n-ary fixpoints ?? sure we can set the fixpoints exp(L) = L at oo i but how about the fixpoints of exp(exp(.. q)) = q and limit cycles of the exp iterations ... e.g. let e^q1 = q2 , e^q2 = q1 , if we want half-iterates , 1/3 iterates and sqrt(2) iterates to have the same fixpoints , this is a problem , not ? perhaps we can 'hide' L at +/- oo i ( like kouznetsov ) and 'hide' the other points at - oo ?? (question 4) do all 'analytic in the neigbourhood of the positive reals' sexp have the fixpoints exp(L) = L at oo i ? ( i know that [L,sexp(slog(L)+o(1))] cannot be in the analytic zone , but maybe [L,sexp(slog(L)+o(1))] isnt part of the analytic zone ) (question 5) slog(z) base x is not holomorphic in x in a domain containing the interval [a,b] if eta is between a and b. why is that ? i know that the real fixpoint dissappears but still ... sorry if those are FAQ or trivial Q. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread some questions about sexp - by tommy1729 - 06/28/2010, 11:18 PM RE: some questions about sexp - by tommy1729 - 06/29/2010, 10:55 PM RE: some questions about sexp - by bo198214 - 07/01/2010, 09:39 AM RE: some questions about sexp - by mike3 - 07/01/2010, 11:05 AM RE: some questions about sexp - by bo198214 - 07/02/2010, 07:14 AM RE: some questions about sexp - by tommy1729 - 07/01/2010, 10:06 PM RE: some questions about sexp - by mike3 - 07/01/2010, 10:28 PM RE: some questions about sexp - by bo198214 - 07/02/2010, 07:17 AM RE: some questions about sexp - by mike3 - 07/02/2010, 07:55 AM RE: some questions about sexp - by tommy1729 - 07/02/2010, 12:27 PM RE: some questions about sexp - by sheldonison - 07/02/2010, 03:52 PM RE: some questions about sexp - by tommy1729 - 07/05/2010, 09:59 PM RE: some questions about sexp - by sheldonison - 07/06/2010, 01:45 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) tommy1729 0 1,592 09/06/2016, 04:23 PM Last Post: tommy1729 Can sexp(z) be periodic ?? tommy1729 2 3,866 01/14/2015, 01:19 PM Last Post: tommy1729 pseudo2periodic sexp. tommy1729 0 1,832 06/27/2014, 10:45 PM Last Post: tommy1729 [2014] tommy's theorem sexp ' (z) =/= 0 ? tommy1729 1 2,854 06/17/2014, 01:25 PM Last Post: sheldonison Multiple exp^[1/2](z) by same sexp ? tommy1729 12 13,869 05/06/2014, 10:55 PM Last Post: tommy1729 entire function close to sexp ?? tommy1729 8 9,578 04/30/2014, 03:49 PM Last Post: JmsNxn Is sexp(z) pseudounivalent for Re(z) > 0 ? tommy1729 3 3,438 03/26/2014, 01:24 PM Last Post: tommy1729 Vincent's theorem and sin(sexp) ? tommy1729 0 1,745 03/22/2014, 11:46 PM Last Post: tommy1729 sexp for base (1/e)^e ~= 0.0660? sheldonison 10 11,051 11/22/2013, 11:20 PM Last Post: mike3 tetration base conversion, and sexp/slog limit equations sheldonison 44 55,470 02/27/2013, 07:05 PM Last Post: sheldonison

Users browsing this thread: 1 Guest(s)