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    I was trying to express real zeros of the equation x^3+mx-1 as continued fractions and I came up with the following recursion method.
    a_1m^1+a_0=a_2, a_2m^2+a_1=a_3, a_n-1m^(n-1)+a_n-2=a_n
    k_1m^1+k_0=k_2, k_2m^2+k_1=k_3, k_n-1m^(n-1)+k_n-2=k_n.
    For m any non-zero positive integer and a_0=1, a_1=0, k_0=0, k_1=1 I was able to predict the result of k_n/a_n. For any other pair of values a_0≠a_1 and k_0≠k_1 the result is unpredictable. Does anyone know if it is possible to predict the numerical value of the ratio k_n/a_n for such pairs?
    If the question is not acceptable, how can I improve it?
    • CommentAuthorgrp
    • CommentTimeDec 23rd 2011
    It would help readers of meta if you followed a format like:
    Is the following question acceptable for posting on MathOverflow?

    <body of question>

    If it is not acceptable, how can it be improved?

    Your current question looks clear and understandable, except the formatting on meta makes it unclear to me whether
    it is two sets of three equations each (e.g X=Y, Z=W, V=a_n) , or two sets of multiple relations (e.g. X=Y=Z=a_n). To answer your question, you might consider drawing some kind of phase diagram for a system related to these recurrences like (x,y) goes (xm^i +a ,ym^i +b), and see if such a picture offers insight. Also, you might ask the question slightly differently, as in "Can one find the set of initial values (a_0,k_0,a_1,k_1) so that the sequence of values (k_n/a_n) converges, and can that limit of convergence be easily expressed in terms of the initial values?"

    Gerhard "Ask Me About System Design" Paseman, 2011.12.23

    Dear Vassilis,

    Unless I am mistaken, this is a duplicate of your previous post on meta. Do you understand that I see this as spamming our site, and extremely unwelcome?

    Sincerely, Scott Morrison

    Dear Scott,

    I thought that because I was suspended, members had considered the previous post closed. Because I am looking for answers I thought asking again was the right way to reopen the discussion. I certainly did not intend to spam the site.

    Dear Gerhard,

    Thank you for your helpful comments. I will edit the formatting. I think "(e.g X=Y, Z=W, V=a_n)" would complicate the question

    I still do not know if I am allowed to post my question. Can you please give me a definitive answer?