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ajsteinmetz · May 26, 2023 · a4df558 · a4df558
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diff --git a/a-short-survey-arxiv/a-short-survey-arxiv.tex b/a-short-survey-arxiv/a-short-survey-arxiv.tex
@@ -860,7 +860,7 @@ \subsection{Electron-positron statistical physics}\label{sec:Partition}
 where we define 
 \begin{align}
  \label{FreePart}&\ln\mathcal{Z}_{free}=\frac{T^3V}{2\pi^2}\left[2\cosh{\left(\frac{\eta_{e}}{T}\right)}\right]\sum_{i=\pm}x_i^2K_2\left(x_i\right)\,,\qquad x_i=\frac{\tilde{m}_i}{T}\\
- \label{MagPart}&\ln\mathcal{Z}_B=\frac{eBTV}{2\pi^2}\left[2\cosh{\left(\frac{\eta_{e}}{T}\right)}\right]\sum_{i=\pm}\bigg[\frac{x_i}{2}K_1\left(x_i\right)+\frac{k^2b_0}{12}K_0\left(x_i\right)\bigg]\,,\\
+ \label{MagPart}&\ln\mathcal{Z}_B=\frac{eBTV}{2\pi^2}\left[2\cosh{\left(\frac{\eta_{e}}{T}\right)}\right]\sum_{i=\pm}\bigg[\frac{x_i}{2}K_1\left(x_i\right)+\frac{b_0}{12}K_0\left(x_i\right)\bigg]\,,\\
  \label{ErrorPart}&\ln\mathcal{Z}_R=\frac{eBTV}{\pi^2}\left[2\cosh{\left(\frac{\eta_{e}}{T}\right)}\right]R.
 \end{align}
 where $R$ is the error remainder which is defined by integrals over Bernoulli polynomials.