Dear Minh,
>
> > OK, I understand that sage do not kown how to evaluate
> > sum(1/(1+k^2), k, -oo, oo)
>
> > But it answer 0 , that is wrong!!!
>
> Both Sage 4.3.3 and 4.3.4 give the same wrong answer:
>
> [mv...@sage sage-4.3.4]$ sage
> ----------------------------------------------------------------------
> | Sage Version 4.3.3, Release Date: 2010-02-21 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> sage: k = var("k")
> sage: sum(1/(1+k^2), k, -oo, oo)
> 0
>
> [mv...@sage sage-4.3.4]$ ./sage
> ----------------------------------------------------------------------
> | Sage Version 4.3.4, Release Date: 2010-03-19 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> sage: k = var("k")
> sage: sum(1/(1+k^2), k, -oo, oo)
> 0
>
> Here is the answer from Maple:
>
> [mv...@sage ~]$ maple
> |\^/| Maple 12 (X86 64 LINUX)
> ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
> \ MAPLE / All rights reserved. Maple is a trademark of
> <____ ____> Waterloo Maple Inc.
> | Type ? for help.> sum(1 / (1 + k^2), k=-infinity..infinity);
>
> Pi coth(Pi)
>
> And the answer from Mathematica:
>
> [mv...@sage ~]$ math
> Mathematica 6.0 for Linux x86 (64-bit)
> Copyright 1988-2007 Wolfram Research, Inc.
>
> In[1]:= Sum[1 / (1 + k^2), {k, -Infinity, Infinty}]
>
> I
> Out[1]= - (PolyGamma[0, -I - Infinty] - PolyGamma[0, I - Infinty])
> 2
>
> > (I have yet 4.3.1; I'm waiting 4.3.4 to update my sage)
>
> Unfortunately, updating to Sage 4.3.4 won't even fix the above issue
> with the sum() command. The above issue with the sum() command is now
> tracked at ticket #8582:
>
> http://trac.sagemath.org/sage_trac/ticket/8582
>
Thanks for include it as a ticket.
Juan Luis
PD: Mathematica 7.0 also gives the correct answer Pi Coth[Pi]]
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