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Re: How to use SeriesCoefficient to define new functions


Hi Liu Xiaojun,

You don't need to uses Series before you uses SeriesCoefficient.
SeriesCoefficient can actually return the general coefficient as a DifferenceRoot object. So you could simply use the following:

p[n_][x1_, x2_, x3_] := 
 Block[{k}, SeriesCoefficient[Exp[x1*k + x2*k^2 + x3*k^3], {k, 0, n}]]

I've used k instead of lambda and I've wrapped the right-hand-side in Block, just in case k has a value already. The first 10 functions can be found using

Table[p[i][x, y, z], {i, 1, 10}] // Simplify

Note: your original code will work if change your SetDelayed := to just Set 
p2[x1_, x2_, x3_] =  SeriesCoefficient[SchurGenerator, {\[Lambda], 0, 2}]

Simon



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