Re: How to use SeriesCoefficient to define new functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg122855] Re: How to use SeriesCoefficient to define new functions*From*: Xiaojun <tigertooth4 at gmail.com>*Date*: Sat, 12 Nov 2011 07:36:00 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <j9b6vs$4u6$1@smc.vnet.net> <j9gf1h$p6l$1@smc.vnet.net>

Simon and Dan, thank you all for your answers:) my problem solved! On Nov 10, 8:11 pm, Dan <dfla... at rcn.com> wrote: > On Nov 8, 7:23 am, Xiaojun <tigertoo... at gmail.com> wrote: > > > > > > > > > > > Hi, > > > I want to define new functions from the =EB-expansion of an exponential > > function as follows: > > > SchurGenerator := Normal[Series[ Exp[x1*=EB + x2*=EB^2 + x3*=EB^3], {=EB, 0, > > 3}]]. > > > Each coefficient may define a function of x1, x2, and x3, which I > > think should be expressed > > as, for example: > > > p2[x1_, x2_, x3_] := SeriesCoefficient[SchurGenerator, {=EB, 0, 2}]. > > > However, it doesn't seem to work. Since the expected output of > > p2[y1,y2,y3] should be > > > y1^2/2 + y2. But the real output is still x1^2/2 + x2. > > > How to define new functions from the expansion coefficients? I > > appreciate your help ! > > > -- > > Best wishes, > > Liu Xiaojun > > Liu, your problem is that your definition for SchurGenerator uses the > literal symbols x1, x2, and x3. If you want to define it so that you > substitute a different symbol when called you will have to use > patterns, as in > > SchurGenerator[x1_,x2_,x3_]:=Normal@Series[Exp[x1*lambda + x2*lambda^2 > + x3*lambda^3],{lambda,0,3}] > > so that p2 becomes > > p2[x1_,x2_,x3_]:=SeriesCoefficient[SchurGenerator[x1,x2,x3],{lambda, > 0,2}]