Re: power series in more than one variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg55713] Re: [mg55679] power series in more than one variables*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Mon, 4 Apr 2005 00:59:18 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

Clear[mySeries]; mySeries[func_, var:{__Symbol},n_Integer]:= Plus@@(Cases[Expand@Normal@ Series[func/.Thread[var->h*var], Sequence@@Thread[{var,0,n}]],_*h^n]/.h->1); mySeries[f[x,y,z],{x,y,z},2] (1/2)*Derivative[2, 0, 0][f][0, 0, 0]*x^2 + z*Derivative[1, 0, 1][f][0, 0, 0]*x + y*Derivative[1, 1, 0][f][0, 0, 0]*x + (1/2)*z^2*Derivative[0, 0, 2][f][0, 0, 0] + y*z*Derivative[0, 1, 1][f][0, 0, 0] + (1/2)*y^2*Derivative[0, 2, 0][f][0, 0, 0] Bob Hanlon > > From: "Christoph Lhotka" <lhotka at astro.univie.ac.at> To: mathgroup at smc.vnet.net > Date: 2005/04/03 Sun AM 05:50:48 EDT > To: mathgroup at smc.vnet.net > Subject: [mg55713] [mg55679] power series in more than one variables > > Hello ! > > How can I define a power series in Mathematica with more than more variables > (x,y,z,...), where only terms x^k*y^l*z^m*..., where k+l+m+...=N should be > considered? I havwe tried Series[exp,{x,..},{y,...},...] but this only returns > nested taylor series. My usual approach is to define an artificial > perturbation parameter, say lambda^k+l+m, holding terms of equal powers > together, but this is not satisfying when only dealing with numerical series, > where the coefficients should only be numeric not mixed symbolic (defining it > this way will give you as third argument to SeriesData non numerical entries. > > Does anyone have some sugestions? > > -- Christoph Lhotka -- > University of Vienna > Institute for Astronomy > Tuerkenschanzstr. 17 > 1180 Vienna, Austria > mail. lhotka at astro.univie.ac.at > >