       Re: Simplifying the *Individual Coefficients* in Series Expansions?

• To: mathgroup at smc.vnet.net
• Subject: [mg35219] Re: Simplifying the *Individual Coefficients* in Series Expansions?
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 3 Jul 2002 05:13:15 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <afrh3q\$lu4\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

Collect[fS,x,Simplify]

??

Because

"Collect[expr, x] collects together terms involving the same powers of \
objects matching x. Collect[expr, {x1, x2, ... }] collects together
terms \
that involve the same powers of objects matching x1, x2, ... .

Collect[expr, var, h] applies h to the expression that forms the
----------------------------------------------------------------
coefficient of each term obtained"
---------------------------------

Regards
Jens

AES wrote:
>
> I have a long expression  f   that involves integers times various
> powers of symbols  b  and  x, i.e.
>
>     f = ratio of two lengthy polynomials in  b  and  x
>
> If I series expand this in  x , viz.
>
>     fS  = Series[f,  {x, 0, 2}] // Normal
>
> I get an answer in the form
>
>     fS =  c1 x + c2 x^2
>
> where the coefficients  c1  and  c2   in the resulting series expansion
> come out as rather messy expressions (ratios of polynomials).  In my
> problem, however, these coefficients actually happen to simplify
> substantially (since there are common factors in their numerators and
> denominators), and I'd like to have them in simplified form.  But if I
> write
>
>     fS // Simplify
>
> I'm back in lengthy polynomial form; and if I try something like
>
>     fS = (Coefficient[fS, x] // Simplify) x +
>                                 (Coefficient[fS, x^2] // Simplify) x^2
>
> I get an expression that looks great, but will not evaluate numerically.
>
> Any easy way around this?

```

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