Vladimir Bondarenko <vb@[EMAIL PROTECTED]
> wrote:
> -----------------------------------------------------------------
>
> N[ ( 4 Catalan + 3 Pi Log[5] - 2 ArcTan[2] Log[5] - 2 I
> PolyLog[2, 2/5 - I/5] + 2 I PolyLog[2, 2/5 + I/5] )/4 ]
>
> NIntegrate[Log[1 + z^2]/(2 - 2 z + z^2), {z, 0,Infinity}]
>
> 3.56442
> 3.56442
>
> -----------------------------------------------------------------
>
> Integrate[Log[1 + z^2]/(2 - 2 z + z^2), {z, 0, Infinity}]
>
> -----------------------------------------------------------------
> VERSION OUTPUT RESOLUTION
> -----------------------------------------------------------------
>
> Mathematica 6.0 -1.49177 <-------------------------------- BUG
>
> Mathematica 5.2 Correct answer OK
>
> Mathematica 4.2 Correct answer OK
>
> Mathematica 3.0 Unevaluated integral OK
>
> -----------------------------------------------------------------
A correct answer, exactly as shown by VB above as the argument of N, can
easily be obtained from the current version of Mathematica: just get
Integrate[Log[1 + z^2]/(2 - 2 z + z^2), z]
and then apply Newton-Leibniz and FullSimplify. Of course, that hardly
excuses the current bug. Is it perhaps due to a convolution problem?
David
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