Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear recurrence with polynomial coefficients

  1. Jul 7, 2011 #1
    Hi all,

    I came across a linear recurrence with polynomial coefficients and realized that I don't have a clue as to how to solve it. The usual methods like generating functions or guessing seem not to work in that case.

    Here is the equation:

    [tex]
    i (i - 1) (i - 2) b = 1/3 (i + 1) i (1 - i) b[i - 3] + (1 + i) i (i - 2) b[i - 2] + (i + 1) (i - 1) (i - 2) b[i - 1]
    [/tex]


    Is there any general theory on recursions of that type or maybe even a general algorithm to compute the solution (in terms of some initial valeus b[0], b[1], b[2])?

    Thanks a lot!

    Pere
     
  2. jcsd
  3. Jul 8, 2011 #2
    So, for this particular recursion, the substitution [itex]b\mapsto(i+1)c[/itex] reduces the equation to a very easy form. The question about the general theory remains.
     
    Last edited: Jul 8, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook