Can Mathematica do this (infinite series)?

*To*: mathgroup at smc.vnet.net*Subject*: [mg113381] Can Mathematica do this (infinite series)?*From*: Sam Takoy <sam.takoy at yahoo.com>*Date*: Tue, 26 Oct 2010 05:34:18 -0400 (EDT)

Hi, I'm working on a project involving infinite series and I don't know how to do it or even ask a sensible question about it. So I cooked up a question the answer to which might give me ideas. f[x_]:=Sum[c[n]x^n, {n, 1, Infinity}] What's the infinite series for f[x]^2 + Sin[x]f[x] in terms of c[n]? What's the simplest way that Mathematica can answer this question for general c[n]? The pipe dream is this: f[c_][x_] := Sum[c[n] x^n, {n, 1, Infinity}] g[c_][x_] := f[c][x]^2 + Sin[x] f[c][x] d[c_][n_] := SeriesCoefficient[g[c][x], {x, 0, n}] d[Log[# + 1/3]/Factorial[#] &][5] // N Thanks, Pavel