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Help to find the upper bound

  1. Aug 12, 2005 #1
    Dear members,

    I try to find the upper bound of the following function. Can anybody gives a hint? Thanks!

    [tex]
    f(t,p)=\sum_p \frac{p(1-p)}{t^5}[p^4(9t^4-81t^3+225t^2-274t+120)+p^3(-12t^4+129t^3-400t^2+524t-240)+
    [/tex]
    [tex]
    \mbox{\hspace{2cm}}p^2(4t^4-59t^3+ 216t^2-311t+150)+p(7t^3-36t^2+59t-30)+(t-1)^2]
    [/tex]
    where
    [tex]
    t=1,2,3,..
    [/tex]
    [tex]
    \sum_p p = 1
    [/tex]

    The problem is to find the function g(t) that
    [tex]
    f(t,p) \leq g(t)
    [/tex]
    It seems that
    [tex]
    g(t)\sim 1/t
    [/tex]
    Is it possible to find a better bound?
     
    Last edited: Aug 12, 2005
  2. jcsd
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