Due diligence first. The first term of the first equation you wrote is missing a sign, as you should have easily checked yourself, from the coefficient of $\ln ~ \pi$. That is, Write down $W(q)$ right above the equation you start with, around your minimum q =2, i.e. $q\equiv 2(1+\epsilon)$, so that $p= 2(1-\epsilon) +O(\epsilon^2)$, dismissing any higher orders of $\epsilon$.

The relevant term for the derivative w.r.t. $2\epsilon$ then is $\pi^{-n2\epsilon/4} N$, so you may catch the paper's typo.

Due diligence first. The first term of the first equation you wrote is missing a sign, as you should have easily checked yourself, from the coefficient of $\ln \pi$. 

That is, write down the parent $W(q)$ right above the equation you start with, around your minimum q =2, i.e. $q\equiv 2(1+\epsilon)$, so that $p= 2(1-\epsilon) +O(\epsilon^2)$, dismissing any higher orders of $\epsilon$.

The relevant term for the derivative w.r.t. $2\epsilon$ then is $\pi^{-n2\epsilon/4} N$, so you may catch that paper's typo.

Due diligence first. The first term of the first equation you wrote is missing a sign, as you should have easily checked yourself, from the coefficient of $\ln ~ \pi$. That is, Write down $W(q)$ right above the equation you start with, around your minimum q =2, i.e. $q\equiv 2(1+\epsilon)$, so that $p= 2(1-\epsilon) +O(\epsilon^2)$, dismissing any higher orders of $\epsilon$.

The relevant term in the derivative w.r.t. $2\epsilon$ then is $\pi^{-n2\epsilon/4} N$, so you catch the paper's typo.

Due diligence first. The first term of the first equation you wrote is missing a sign, as you should have easily checked yourself, from the coefficient of $\ln ~ \pi$. That is, Write down $W(q)$ right above the equation you start with, around your minimum q =2, i.e. $q\equiv 2(1+\epsilon)$, so that $p= 2(1-\epsilon) +O(\epsilon^2)$, dismissing any higher orders of $\epsilon$.

The relevant term for the derivative w.r.t. $2\epsilon$ then is $\pi^{-n2\epsilon/4} N$, so you may catch the paper's typo.