Generating function help plz

• Sep 23rd 2008, 01:42 PM
jmmjm
Generating function help plz
Hi, I am encountering this problem:

Let a0, a1, a2.... be an infinite sequence of non-negative integers and A(x) = the summation of an * x^n is the corresponding generating function.

Express the following sequences in terms of A(x), and it should not contain a summation symbol or an infinite sum:
c) a0, 0, a2, 0 , a4, 0, a6.........
d) a0, 2a1, 4a2, 8a3, 16a4........

I have thought so hard but still nothing come out form my mind. thanks in advance.
• Sep 23rd 2008, 02:04 PM
jmmjm
for part d), is it just A(2x) ? This is also the expression in terms of A(x), right?
• Sep 24th 2008, 08:23 AM
wisterville
Hello,

You are right. For (c), compute A(-x).

Bye.
• Sep 24th 2008, 09:02 AM
bkarpuz
Quote:

Originally Posted by jmmjm
Hi, I am encountering this problem:

Let a0, a1, a2.... be an infinite sequence of non-negative integers and A(x) = the summation of an * x^n is the corresponding generating function.

Express the following sequences in terms of A(x), and it should not contain a summation symbol or an infinite sum:
c) a0, 0, a2, 0 , a4, 0, a6.........
d) a0, 2a1, 4a2, 8a3, 16a4........

I have thought so hard but still nothing come out form my mind. thanks in advance.

Do you mean $\displaystyle A(x)=\bigg(\sum\limits_{i=0}^{n}a_{i}\bigg)x^{n}$?
• Sep 25th 2008, 07:19 AM
wisterville
Hello,

No, I replied thinking that jmmjm meant $\displaystyle A(x)=\sum_{n=0}^{\infty}a_nx^n$.

Bye.