Re: What am I doing wrong?

• To: mathgroup at smc.vnet.net
• Subject: [mg91601] Re: What am I doing wrong?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 28 Aug 2008 07:40:21 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g95k5j\$51m\$1@smc.vnet.net>

```Jack L Goldberg 1 wrote:
> In(1)  SeriesCoefficient[1/(1-x),{x,0,n}]
>
> Out(1)  (-1)^n*Binomial[-1,n]
>
> Next,
>
> In(2)   FunctionExpand[(-1)^n*Binomial[-1,n],Assumptions->Element[n,Integers]]
>
> OUt(2)  ComplexInfinity
>
> In(3)   Table[(-1)^n*Binomial[-1,n], {n,-2,2}]
>
> Out(3)  {0,0,1,1,1}
>
> Incidentally, FullSimplify in place of FunctionExpand yields the same
> result of FunctionExpand and FullSymplify resorting to the Gamma
> Function for the simplification?
>
> Is this a bug or a feature?
>
> Thanks,
>
> Jack

You should tell Mathematica that n is a non-negative integer:

In[1]:= Assuming[Element[n, Integers] && n >= 0,
FunctionExpand[(-1)^n*Binomial[-1, n]]]

Out[1]= (-1)^(2 n)

In[2]:= Assuming[Element[n, Integers] && n < 0,
FunctionExpand[(-1)^n*Binomial[-1, n]]]

Out[2]= -1

In[3]:= Assuming[Element[n, Integers] && n >= -3,
FunctionExpand[(-1)^n*Binomial[-1, n]]]

Out[3]= ComplexInfinity

Regards,
-- Jean-Marc

```

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