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.