06/07/2011, 09:02 PM
im sorry
i do not wish to be annoying.
but this does not seem like a new idea.
in fact , it seems mine :
quoting from my own posts :
thread tid 474 posted on 7/11/10 title : tommy's uniqueness conditions
post nr 1 , thread started by me :
" i partially already mentioned the first uniqueness condition before :
d f^n / d x^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k.
and probably ( i.e. if im not mistaken because of the local heat wave )this is true if and only if the following is true :
( i.e. i assume " equivalent to " )
d f^n / d k^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k. "
thread tid 484 posted on 7/29/10 title : final uniqueness condition ... probably
post nr 1 , thread started by me :
" d f^2 / d x^2 sexp(slog(x) + k) > 0 for all real x and all real k with 0 < k < Q where Q is any nonzero positive real.
assuming sexp resp slog to be C^2 of course , i 'believe' this condition implies analytic as well.
is this equivalent to d f^2 / d x^2 sexp(x) > 0 for all positive real x ?
i assume because of the substitution x = sexp(y) "
if you combine those two posts , i find it pretty clear that the idea has occured to me first.
notice that exp^[t](x) is equivalent to sexp(slog(x) + t)
despite one of those threads and this one contains mistakes , that idea is clearly mine. ( i even did a search on this forum too see if anyone else was first and looked on sci.math , mathoverflow , google and some books )
i believe my (tommy's) 2sinh method satisfies these conditions and hence it is conjectured for bases > sqrt(e) [ thus including e like mike ]
( yes these posts were made after i posted the 2sinh method - which is also by me and in fact way older than this forum ( i found it in my teenage notes ) and i mentioned that too )
thus for bases > sqrt(e) =>
d f^n / d x^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k.
d f^n / d k^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k.
d f^2 / d x^2 sexp(slog(x) + k) > 0 for all real x and all real k with 0 < k < Q where Q is any nonzero positive real.
are all ideas of me , somewhat sloppy ( i could have written positive real k e.g. ) but mine.
so basicly my opinion is that this conjecture of mike is actually a rewording of some of my conjectures.
regards
tommy1729
i do not wish to be annoying.
but this does not seem like a new idea.
in fact , it seems mine :
quoting from my own posts :
thread tid 474 posted on 7/11/10 title : tommy's uniqueness conditions
post nr 1 , thread started by me :
" i partially already mentioned the first uniqueness condition before :
d f^n / d x^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k.
and probably ( i.e. if im not mistaken because of the local heat wave )this is true if and only if the following is true :
( i.e. i assume " equivalent to " )
d f^n / d k^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k. "
thread tid 484 posted on 7/29/10 title : final uniqueness condition ... probably
post nr 1 , thread started by me :
" d f^2 / d x^2 sexp(slog(x) + k) > 0 for all real x and all real k with 0 < k < Q where Q is any nonzero positive real.
assuming sexp resp slog to be C^2 of course , i 'believe' this condition implies analytic as well.
is this equivalent to d f^2 / d x^2 sexp(x) > 0 for all positive real x ?
i assume because of the substitution x = sexp(y) "
if you combine those two posts , i find it pretty clear that the idea has occured to me first.
notice that exp^[t](x) is equivalent to sexp(slog(x) + t)
despite one of those threads and this one contains mistakes , that idea is clearly mine. ( i even did a search on this forum too see if anyone else was first and looked on sci.math , mathoverflow , google and some books )
i believe my (tommy's) 2sinh method satisfies these conditions and hence it is conjectured for bases > sqrt(e) [ thus including e like mike ]
( yes these posts were made after i posted the 2sinh method - which is also by me and in fact way older than this forum ( i found it in my teenage notes ) and i mentioned that too )
thus for bases > sqrt(e) =>
d f^n / d x^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k.
d f^n / d k^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k.
d f^2 / d x^2 sexp(slog(x) + k) > 0 for all real x and all real k with 0 < k < Q where Q is any nonzero positive real.
are all ideas of me , somewhat sloppy ( i could have written positive real k e.g. ) but mine.
so basicly my opinion is that this conjecture of mike is actually a rewording of some of my conjectures.
regards
tommy1729