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Re: What am I doing wrong?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91612] Re: What am I doing wrong?
  • From: Jack L Goldberg 1 <jackgold at umich.edu>
  • Date: Fri, 29 Aug 2008 04:10:55 -0400 (EDT)
  • References: <g95k5j$51m$1@smc.vnet.net> <48B679EA.6000300@gmail.com>

Thanks Jean-Marc. I cannot understand why I didn't add n > 0 as part 
of my use of assumptions. This solves the problem I was working on, 
however, read the following:

There still remains one issue.
For negative integers (-1)^n*Binomial[-1,n] returns 0, witness the output of

Table[ (-1)^n*Binomial[-1,n], {n,-10,-1], say. So,

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

So it appears that the simplification process does not like negative 
integers as the first argument to Binomial, but the code that 
evaluates Binomial doesn't mind it at all.  This same result occurs 
for (-1)^n Binomial[-m,n] when m is any negative integer.
Jack

Quoting Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>:

> 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, ComplexInfinity.  I wonder if this misleading answer 
>> is a  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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