       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[#] &] // N

Thanks,

Pavel

```

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