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>*Reply-to*: comp.soft-sys.math.mathematica at googlegroups.com

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