• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 open problems survey bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 05/31/2011, 04:54 PM (This post was last modified: 05/31/2011, 07:04 PM by bo198214.) In generalization of (the already solved) TPID 6 and following this thread of Andrew: Does the sequence of interpolating polynomials of the points $(0,0),(1,y_1),\dots,(n,y_n)$ defined by $y_n [4] n = n$ pointwise converge to a function $f$ on (0,oo) (, satisfying $f(n)=y_n$)? If it converges: a) is then the limit function $f$ analytic, particularly at the point $x=\eta$? b) For $b\le \eta$ let b[4]x be the regular superexponential at the lower fixpoint. Is then f(x)[4]x = x for non-integer x with $f(x)\le\eta$? c) For $b> \eta$ let b[4]x be the super-exponential via Kneser/perturbed Fatou coordinates. Is then f(x)[4]x = x for non-integer x with $f(x)>\eta$? To be more precise we can explicitely give the interpolating polynomials: $f_N(x) = \sum_{n=0}^N \left(x\\n\right) \sum_{m=0}^n \left(n\\m\right) (-1)^{n-m} y_m$, the question of this post is whether $\lim_{n\to\infty} f_n(x)$ exists for each $x>0$. « Next Oldest | Next Newest »

 Messages In This Thread open problems survey - by bo198214 - 05/17/2008, 10:03 AM eigenvalues of Carleman matrix for b^x, TPID 1 - by bo198214 - 05/17/2008, 10:23 AM Exponential Factorial, TPID 2 - by andydude - 05/26/2008, 03:24 PM eigenvalues of Carleman matrix for (x+s)^p-s, TPID 3 - by bo198214 - 06/29/2008, 12:36 PM Existence of bounded b^z TPID 4 - by bo198214 - 10/08/2008, 04:22 PM sqrt(2) tetrational is completely discontinuous TPID 5 - by bo198214 - 05/01/2009, 09:20 AM Limit of self-super-roots is e^1/e. TPID 6 - by andydude - 10/07/2009, 12:03 AM A conjecture on bounds. TPID 7 - by andydude - 10/23/2009, 05:27 AM Elementary superfunction of polynomial without real fixed points TPID 8 - by bo198214 - 04/25/2010, 10:53 AM Logarithm reciprocal TPID 9 - by bo198214 - 07/20/2010, 05:50 AM Convergence of Eulers and Etas. TPID 10 - by dantheman163 - 10/31/2010, 07:13 PM RE: open problems survey - by nuninho1980 - 10/31/2010, 09:50 PM Tommy's conjecture about Eulers and Etas. TPID 11. - by tommy1729 - 12/01/2010, 03:56 PM convergence of self-tetra-root polynomial interpolation. TPID 12 - by bo198214 - 05/31/2011, 04:54 PM convergence of self-root polynomial interpolation. TPID 13 - by bo198214 - 05/31/2011, 07:02 PM Tommy's conjecture about andrew slog method. TPID 14 - by tommy1729 - 06/01/2011, 06:23 PM Tommy's conjecture TPID 16 - by tommy1729 - 06/07/2014, 10:44 PM Error terms for fake function theory TPID 17 - by tommy1729 - 03/28/2015, 10:48 PM The third super-root TPID 18 - by andydude - 12/25/2015, 06:16 AM

 Possibly Related Threads... Thread Author Replies Views Last Post open problems / Discussion Gottfried 8 9,751 06/26/2008, 07:20 PM Last Post: bo198214

Users browsing this thread: 1 Guest(s)