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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
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