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On the attached picture I've highlighted the term which I do not agree with. Is it actually true ? In my calculations I get $$-n(\frac{1}{2}\log(\sqrt{2\pi})+\log(\sigma)),$$ instead. Thank you in advance.

enter image description here

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    $\begingroup$ Notice that $0.5 \log(\sigma^2)=\log(\sigma)$. So $\sigma$ terms coincide. $\log \pi$ is often omitted because this is a constant not affecting anything. But formally speaking you are correct.Nevertheless log-likelihood is often claimed to be defined up to constant addend. $\endgroup$ – Alexander Vigodner Sep 12 '14 at 15:44

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