a curious answer
- To: mathgroup at smc.vnet.net
- Subject: [mg69055] a curious answer
- From: "rick" <awass at umich.edu>
- Date: Tue, 29 Aug 2006 03:25:34 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
Can anyone explain these answers (Out[5] and Out[6])?
Line 1 defines a polynomial in x that depends on n;
line 2 tests the definition when n= 4;
line 3 lists the coefficients of that polynomial and
line 4 checks the list when n= 4; lines 5 and 6 ask for a closed form
for the polynomial and coefficients (which is probably not possible). I
expected no answer-not gibberish.
In[1]:=
k[n_]:=Expand[Product[(j*x+n-j),{j,1,n-1}]]
In[2]:=
k[4]
Out[2]=
\!\(6 + 26\ x + 26\ x\^2 + 6\ x\^3\)
In[3]:=
cL[s_]:=CoefficientList[k[s],x]
In[4]:=
cL[4]
Out[4]=
{6,26,26,6}
In[5]:=
cL[n]
Out[5]=
\!\({\(-\((\(-1\))\)\^n\)\ n\^\(\(-1\) + n\)\ \(\((\(-1\) + n)\)!\)}\)
In[6]:=
k[n]
Out[6]=
\!\(\(-\((\(-1\))\)\^n\)\ n\^\(\(-1\) + n\)\ \(\((\(-1\) + n)\)!\)\)
Thanks,
- Follow-Ups:
- Re: a curious answer
- From: Devendra Kapadia <dkapadia@wolfram.com>
- Re: a curious answer
- From: "Chris Chiasson" <chris@chiasson.name>
- Re: a curious answer