07/24/2010, 10:58 PM
http://cdn.bitbucket.org/bo198214/bunch/...s/main.pdf
assuming you mean that , and kouznetsov is equal to " the cauchy integral approach "
i have to say that the last limit formula ( recurrence ) on the bottom of page 20 is not clear to me.
i mean , how does one solve this ?
the tetration is on both sides of the equation , the integral is related to values of the tetration itself ??
i understand very well how you arrive at that last equation.
but not how it helps or needs to solved ?
i want to remark that - though maybe i dont understand well - i do think this 'cauchy' formula is very well suited to compare if 2 functions that are both analytic solutions of tetration are in fact equal or not.
more specificly i intended - and independently of this forum or any papers - to test if my solution is equal to kouznetsov and ' equal to it self ' ( needed to show existance and Coo ) with those integrals.
more specificly , use f1 and f2 ( the 2 solutions to tetration ) on both sides of the equation and see if the equation still holds.
thus f1 on LHS and f2 on RHS for clarity ...
furthermore , im dubious if that equation requires uniqueness ...
i dont see why sexp(x + 1periodic(x) ) wont satisfy the same equation , though maybe there is no uniqueness claim to the cauchy integral approach ? ( but kouznetsov claims uniqueness ... based upon a non-unique cauchy integral equation ?? )
sorry if im slow , but the equation seems as nonconstructive as
log(f(x+1)) = f(x)
adding just a limit and an integral and some extra terms and requiring values of f(x) for certain x ...
i dont want to be harsh , but this is how i feel and understand it , unless explained better ... without C+ or C++ or other computer language plz !!!
regards
tommy1729
assuming you mean that , and kouznetsov is equal to " the cauchy integral approach "
i have to say that the last limit formula ( recurrence ) on the bottom of page 20 is not clear to me.
i mean , how does one solve this ?
the tetration is on both sides of the equation , the integral is related to values of the tetration itself ??
i understand very well how you arrive at that last equation.
but not how it helps or needs to solved ?
i want to remark that - though maybe i dont understand well - i do think this 'cauchy' formula is very well suited to compare if 2 functions that are both analytic solutions of tetration are in fact equal or not.
more specificly i intended - and independently of this forum or any papers - to test if my solution is equal to kouznetsov and ' equal to it self ' ( needed to show existance and Coo ) with those integrals.
more specificly , use f1 and f2 ( the 2 solutions to tetration ) on both sides of the equation and see if the equation still holds.
thus f1 on LHS and f2 on RHS for clarity ...
furthermore , im dubious if that equation requires uniqueness ...
i dont see why sexp(x + 1periodic(x) ) wont satisfy the same equation , though maybe there is no uniqueness claim to the cauchy integral approach ? ( but kouznetsov claims uniqueness ... based upon a non-unique cauchy integral equation ?? )
sorry if im slow , but the equation seems as nonconstructive as
log(f(x+1)) = f(x)
adding just a limit and an integral and some extra terms and requiring values of f(x) for certain x ...
i dont want to be harsh , but this is how i feel and understand it , unless explained better ... without C+ or C++ or other computer language plz !!!
regards
tommy1729