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: owner-wri-mathgroup 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*(k-d)/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*(k-d)/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*(k-d)/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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