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Mathematica and infinite series

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113185] Mathematica and infinite series
  • From: Sam Takoy <sam.takoy at yahoo.com>
  • Date: Sun, 17 Oct 2010 06:06:03 -0400 (EDT)

Hi,

I am about to embark on a project that operates heavily in infinite 
series, so I started figuring out Mathematica's basis capabilities. I 
found them very impressive, but I came across this:


f[x_] := Sum[Log[n]/(n^2 Factorial[n]) x^n, {n, 1, Infinity}]
Assuming[n > 0, SeriesCoefficient[f[x], {x, 0, 4}]]


Answer:

SeriesCoefficient[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(\[Infinity]\)]
\*FractionBox[\(
\*SuperscriptBox[\(x\), \(n\)]\ Log[n]\), \(
\*SuperscriptBox[\(n\), \(2\)]\ \(n!\)\)]\), {x, 0, 4}]


Why doesn't Mathematica produce Log[n]/(n^2 Factorial[n]) as the answer?

Thanks!

Sam


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