Re: Re: power series in more than one variables
- To: mathgroup at smc.vnet.net
- Subject: [mg55716] Re: Re: [mg55679] power series in more than one variables
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 4 Apr 2005 00:59:22 -0400 (EDT)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
This will default the variable list to a list of all non-numeric symbols present in the function Clear[mySeries]; mySeries[func_, n_Integer]:=Module[ {var=Union[Cases[func,_Symbol?(!NumericQ[#]&),Infinity]]}, Plus@@(Cases[Expand@Normal@ Series[func/.Thread[var->h*var], Sequence@@Thread[{var,0,n}]],_*h^n]/.h->1)]; 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); Clear[f,x,y,z]; mySeries[f[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] And@@Table[mySeries[f[x,y,z],n]==mySeries[f[x,y,z],{x,y,z},n],{n,5}] True Bob Hanlon > > From: Bob Hanlon <hanlonr at cox.net> To: mathgroup at smc.vnet.net > Date: 2005/04/03 Sun PM 12:20:21 EDT > To: "Christoph Lhotka" <lhotka at astro.univie.ac.at>, <mathgroup at smc.vnet.net> > Subject: [mg55716] Re: [mg55679] power series in more than one variables > > 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: [mg55716] [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 > > > > >