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Real sum gives complex result > Bug in Mathematica?
 To: mathgroup at smc.vnet.net
 Subject: [mg44493] Real sum gives complex result > Bug in Mathematica?
 From: nsng0203 at web.de (Norbert Schuch)
 Date: Wed, 12 Nov 2003 08:01:41 0500 (EST)
 Organization: GWDG, Goettingen
 Sender: ownerwrimathgroup at wolfram.com
Hi,
the following problems appears with Mathematica 4,0, 4.1, 4.2:
 In[1]:= Sum[Sin[Pi*k/n]*Sin[Pi*(kd)/n],{k,d,n}]/.{d>10,n>100}//N

 Out[1]= 39.4497  25.4353 I

 In[2]:= Sum[Sin[Pi*k/n]*Sin[Pi*(kd)/n],{k,d+1,n}]/.{d>10,n>100}//N

 14
 Out[2]= 47.7141  6.11986 10 I

 In[3]:= Sum[Sin[Pi*k/n]*Sin[Pi*(kd)/n],{k,10,100}]/.{d>10,n>100}//N

 Out[3]= 47.7141
Output 2 and 3 are correct, while output 1 is complex although the sum
is over real contributions! (The difference between 1 and 2 is zero, as
the second sine vanishes.) What is the problem?
Thanks, Norbert
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