Date: Feb 2, 2012 1:48 PM
Author: ganesh
Subject: Re: Integration of O() terms of the Taylor series
Apologies for the display of some of the variables in the equation.

Reposting it.

Hello,

I have two functions say f1(?) and f2(?) as follows:

f1(?)=1/(a?^2) + 1/(b?) + O(1) ... (1)

and

f2(?)= c+d?+O(?^2) ... (2)

where ? = ?-? and a,b,c,d and ? are constants. Eq. (1) and (2) are

the

Taylor series expansions of f1(?) and f2(?) about ? respectively. I

need to integrate f1(?) and f2(?) with respect to ? (-1,1).

Integration is straight forward for all the terms except O(1) and

O(?^2) in (1) and (2) respectively. How do I proceed here to

integrate

the O() terms? If anyone can guide me on this it will be extremely

helpful. Many thanks for the help.

Regards,

N.

On Feb 2, 6:42 pm, GD <gcdi...@gmail.com> wrote:

> Hello,

>

> I have two functions say f1(â) and f2(â) as follows:

>

> f1(â)=1/(aä^2) + 1/(bä) + O(1) ... (1)

>

> and

>

> f2(â)= c+dä+O(ä^2) ... (2)

>

> where ä = â-ç and a,b,c,d and ç are constants. Eq. (1) and (2) are the

> Taylor series expansions of f1(â) and f2(â) about ç respectively. I

> need to integrate f1(â) and f2(â) with respect to â (-1,1).

> Integration is straight forward for all the terms except O(1) and

> O(ä^2) in (1) and (2) respectively. How do I proceed here to integrate

> the O() terms? If anyone can guide me on this it will be extremely

> helpful. Many thanks for the help.

> Regards,

> N.