- #1

phonic

- 28

- 0

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?

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: