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MathGroup Archive 2001

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Re: Expansion Coefficients in Multivariate Series Expansions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26613] Re: [mg26579] Expansion Coefficients in Multivariate Series Expansions?
  • From: BobHanlon at aol.com
  • Date: Thu, 11 Jan 2001 10:39:21 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

f = Sum[
      ToExpression["c" <> ToString[k] <> ToString[m] <> ToString[n]]*x^k*y^m*
        z^n, 
      {k, 0, 2}, {m, 0, 2}, {n, 0, 2}];

seriesExpr = Series[f, {x, 0, 2}, {y, 0, 2}, {z, 0, 2}];

SeriesCoefficient[seriesExpr, {0, 2, 0}]

c020

SeriesCoefficient[seriesExpr, {1, 0, 2}]

c102

g = x*y*E^(a*z)*Cos[n*x];

gSeries = Series[g, {x, 0, 3}, {y, 0, 3}, {z, 0, 4}];

SeriesCoefficient[gSeries, {1, 1, 3}]

a^3/6


Bob Hanlon

In a message dated 2001/1/9 2:40:08 AM, siegman at stanford.edu writes:

>Given an expression that is the sum of products of integer powers of 
>three variables (say x,y,z) multiplied by numerical coefficients:
>
>   f = c000 + c100 x + c010 y + c001 z + c110 x y + c211 x^2 y z + . . . 
>   
>where the  cijk's are all real numbers, and f may or may not be in 
>Normal (or other) form, how do I find the coefficient of a particular 
>term, e.g. c100 for the x term (*not*  c1000 + c110 y), or  ckmn for the
>
>x^k y^m z^n term?
>
>Neither Coefficient nor SeriesCoefficient seems to do this -- and the 
>SeriesCoefficient[expr, {n1,n2,n3,..}] syntax seems to be mentioned but
>neither explained or illustrated in the on-line Help.
>


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