SeriesCoefficient: needs work!

• To: mathgroup at smc.vnet.net
• Subject: [mg83384] SeriesCoefficient: needs work!
• From: jackgold at umich.edu
• Date: Mon, 19 Nov 2007 06:11:24 -0500 (EST)

```Hi Everyone,

I have been experimenting with the new (ver 6) command,
SeriesCoefficient in the form,

SeriesCoefficient[fnt,{x,x0,n}].

Here fnt is a function of x and n is symbolic.  This command is
supposed to return the nth coefficient in the series expansion of fnt

I have found the following results on a MacBook Pro running Tiger.

1) SeriesCoefficient[Cos[x] Exp[x], {x, 0, n}] returns itself, unevaluated.

2) SeriesCoefficient[Cos[x] Exp[x]/(1-x), {x, 0, n}] returns an
expression involving incomplete Gamma functions with an imaginary
argument.  Odd that 1) does not compute but 2) does! Not that the
result is terribly revealing, by the way.

3) SeriesCoefficient[Sin[x] Exp[x], {x, 0, n}] so preposterously
complicated that most of us would have preferred no result!  (Just
joking.  The result is far to complicated to publish here.)

My opinion is that this use of SeriesCoefficient should not be offered
to the public until some of these obvious glitches are cleaned up.
Incidentally, since the nth terms of the individual functions Sin[x],
Cos[x], Exp[x] and 1/(1-x) can be found using SeriesCoefficient and
surely Mathematica knows how to find the nth coefficient of a product of power
series, I suspect the problem lies in the finite summation which
results from the use of the Cauchy product formula.

```

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