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. >