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How to use SeriesCoefficient to define new functions


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



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