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Hypergeometric functions and Sum error in 5.01?

• To: mathgroup at smc.vnet.net
• Subject: [mg51678] Hypergeometric functions and Sum error in 5.01?
• From: "Richard Ollerton" <R.Ollerton at uws.edu.au>
• Date: Fri, 29 Oct 2004 03:38:55 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Mathematica 5.01 produces the following:
In[1]:= s1=Sum[Binomial[n-i,m]2^i,{i,0,n-m}]

Out[1]= Gamma[1+n] Hypergeometric2F1[1,m-n,-n,2] / (Gamma[1+m] Gamma[1-m+n])

In[2]:= Table[{s1,Sum[Binomial[n-i,m]2^i,{i,0,n-m}]}/.n®3,{m,1,3}]

Out[2]= {{-5,11},{-11,5},{-15,1}}

Out[2] compares Mathematica's closed form with actual values.  There appears to be an error in the rules used by Sum when simplifying this expression.
 
Richard Ollerton
r.ollerton at uws.edu.au

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