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Simplifying the *Individual Coefficients* in Series Expansions?

• To: mathgroup at smc.vnet.net
• Subject: [mg35214] Simplifying the *Individual Coefficients* in Series Expansions?
• From: AES <siegman at stanford.edu>
• Date: Tue, 2 Jul 2002 02:12:46 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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?

• Follow-Ups:
  • Re: Simplifying the *Individual Coefficients* in Series Expansions?
    • From: Daniel Lichtblau <danl@wolfram.com>