# Euler-Maclaurin Series formula on an infinite series?

• Sep 16th 2009, 07:41 AM
LatexPineapple
Euler-Maclaurin Series formula on an infinite series?
As this is my first post, I don't exactly expect the group to flock to my aid in any way, but my basic problem is lack of familiarity with the way this formula works. Suppose I have an infinite sum that we accept to be convergent.$\displaystyle sigma(f(x), i=0, inf)$

How does one apply the Euler-Maclaurin formula?

I'd rather not go into details of the function in question, as it is homework, and that would be cheating, and cheating is wrong.
• Sep 16th 2009, 07:55 AM
Jester
(Nerd)
Quote:

Originally Posted by LatexPineapple
As this is my first post, I don't exactly expect the group to flock to my aid in any way, but my basic problem is lack of familiarity with the way this formula works. Suppose I have an infinite sum that we accept to be convergent.$\displaystyle sigma(f(x), i=0, inf)$

How does one apply the Euler-Maclaurin formula?

I'd rather not go into details of the function in question, as it is homework, and that would be cheating, and cheating is wrong.

The formula is

$\displaystyle f(a) + f'(a)(x-a) + f''(a) \frac{(x-a)^2}{2!} + f'''(a) \frac{(x-a)^3}{3!} + \cdots$

Just plug and chug!
• Sep 16th 2009, 07:56 AM
LatexPineapple
you're my savior.