       Re: How to use SeriesCoefficient to define new functions

• To: mathgroup at smc.vnet.net
• Subject: [mg122797] Re: How to use SeriesCoefficient to define new functions
• From: Dan <dflatin at rcn.com>
• Date: Thu, 10 Nov 2011 06:56:53 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j9b6vs\$4u6\$1@smc.vnet.net>

```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
>
> --
> Best wishes,
> Liu Xiaojun

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}]

```

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