Help to find the upper bound

  • Thread starter phonic
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  • #1
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Main Question or Discussion Point

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:

Answers and Replies

  • #2
13,221
10,137
No. Not as long as no additional conditions on ##p## in dependency of ##t## are given. You can assume the worst case of ##\sum_p=p=1## and get ##f(t,1)=O(t^{-1})## so all you can do is finding a better constant.
 

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