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Re: Integration of O() terms of the Taylor series
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GD
Feb 2, 2012, 1:48:34 PM2/2/12
to
Apologies for the display of some of the variables in the equation.
Reposting it.
Hello,
I have two functions say f1(β) and f2(β) as follows:
f1(β)=1/(aδ^2) + 1/(bδ) + O(1) ... (1)
and
f2(β)= c+dδ+O(δ^2) ... (2)
where δ = β-η and a,b,c,d and η are constants. Eq. (1) and (2) are
the
Taylor series expansions of f1(β) and f2(β) about η respectively. I
need to integrate f1(β) and f2(β) with respect to β (-1,1).
Integration is straight forward for all the terms except O(1) and
O(δ^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.
Reposting it.
Hello,
I have two functions say f1(β) and f2(β) as follows:
f1(β)=1/(aδ^2) + 1/(bδ) + O(1) ... (1)
and
f2(β)= c+dδ+O(δ^2) ... (2)
where δ = β-η and a,b,c,d and η are constants. Eq. (1) and (2) are
the
Taylor series expansions of f1(β) and f2(β) about η respectively. I
need to integrate f1(β) and f2(β) with respect to β (-1,1).
Integration is straight forward for all the terms except O(1) and
O(δ^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.
G. A. Edgar
Feb 3, 2012, 9:45:23 AM2/3/12
to
In article
<75f375aa-ec39-4c7f...@hs8g2000vbb.googlegroups.com>, GD
>
> 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).
it is best to stick to only ASCII for posting here. Oldtimers like me
know what "ASCII" means, youngsters may not.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
<75f375aa-ec39-4c7f...@hs8g2000vbb.googlegroups.com>, GD
<gcd...@gmail.com> wrote:
> 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:
> Apologies for the display of some of the variables in the equation.
> Reposting it.
>
> Hello,
>
> 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.
>
>
>
>
I still cannot see the variables. Usenet is an ancient technology, so
> the O() terms? If anyone can guide me on this it will be extremely
> helpful. Many thanks for the help.
> Regards,
> N.
>
>
>
>
it is best to stick to only ASCII for posting here. Oldtimers like me
know what "ASCII" means, youngsters may not.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
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