Re: How to use SeriesCoefficient to define new functions

• To: mathgroup at smc.vnet.net
• Subject: [mg122778] Re: How to use SeriesCoefficient to define new functions
• From: Simon <simonjtyler at gmail.com>
• Date: Thu, 10 Nov 2011 06:53:26 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j9b6vs\$4u6\$1@smc.vnet.net> <j9doq6\$b6c\$1@smc.vnet.net>

```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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