From 1eac59f6b19b3dc3fcb86109113302587f752507 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 25 Oct 2021 14:07:24 +0200
Subject: Finished table of series coefficients.

---
 ising_scaling.tex | 38 +++++++++++++++++++++++---------------
 1 file changed, 23 insertions(+), 15 deletions(-)

(limited to 'ising_scaling.tex')

diff --git a/ising_scaling.tex b/ising_scaling.tex
index ca1bd15..d4ea507 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -582,22 +582,30 @@ accuracy of the fit results can be checked against the known values here.
 \begin{table}\label{tab:fits}
   \begin{tabular}{c|lll}
     $m$ & \multicolumn{1}{c}{$\mathcal F_-^{(m)}$} & $\mathcal F_0^{(m)}$ & $\mathcal F_+^{(m)}$ \\\hline
-    0   & \hphantom{$-$}0                    & $-1.197\,733\,383\,797\ldots$ & \hphantom{$-$}0                    \\
-    1   & $-1.357\,838\,341\,707\ldots$        & \hphantom{$-$}$0.318\,810\,124\,891\ldots$    & \hphantom{$-$}0                    \\
-    2   & $-0.048\,953\,289\,720\ldots$    & \hphantom{$-$}$0.110\,886\,196\,683(2)$     & $-1.845\,228\,078\,233\ldots$     \\
-    3   & \hphantom{$-$}$0.038\,863\,932(3)$         & $-0.016\,426\,894\,65(2)$      & \hphantom{$-$}0                    \\
-    4   & $-0.068\,362\,119(2)$       & $-2.639\,978(1)\times10^{-4}$ & \hphantom{$-$}$8.333\,711\,750(5)$     \\
-    5   & \hphantom{$-$}$0.183\,883\,70(1)$           & \hphantom{$-$}$5.140\,526(1)\times10^{-4}$ & \hphantom{$-$}0                \\
-    6   & $-0.659\,171\,4(1)$          & \hphantom{$-$}$2.088\,65(1)\times 10^{-4}$ & $-95.168\,96(1)$       \\
-    7   & \hphantom{$-$}$2.937\,665(3)$             & \hphantom{$-$}$4.481\,9(1)\times10^{-5}$  & \hphantom{$-$}0                 \\
-    8   & $-15.61(1)$             & \hphantom{$-$}$3.16\times10^{-7}$  & \hphantom{$-$}1457.62(3)              \\
-    9   & \hphantom{$-$}96.76                & $-4.31\times10^{-6}$  & \hphantom{$-$}0                    \\
-    10  & $-679$               & $-1.99\times10^{-6}$ & $-25\,891(2)$               \\
-    11  & \hphantom{$-$}$5.34\times10^3$     &                      & \hphantom{$-$}0                    \\
-    12  & $-4.66\times10^4$    &                      & \hphantom{$-$}$5.02\times10^5$     \\
-    13  & \hphantom{$-$}$4.46\times10^5$     &                      & \hphantom{$-$}0                    \\
-    14  & $-4.66\times10^6$    &                      & $-1.04\times10^7$
+    0 & \hphantom{$-$}0 & $-1.197\,733\,383\,797\ldots$ & \hphantom{$-$}0 \\
+    1 & $-1.357\,838\,341\,707\ldots$ & \hphantom{$-$}$0.318\,810\,124\,891\ldots$ & \hphantom{$-$}0 \\
+    2 & $-0.048\,953\,289\,720\ldots$ & \hphantom{$-$}$0.110\,886\,196\,683(2)$ & $-1.845\,228\,078\,233\ldots$ \\
+    3 & \hphantom{$-$}$0.038\,863\,932(3)$ & $-0.016\,426\,894\,65(2)$ & \hphantom{$-$}0 \\
+    4 & $-0.068\,362\,119(2)$ & $-2.639\,978(1)\times10^{-4}$ & \hphantom{$-$}$8.333\,711\,750(5)$ \\
+    5 & \hphantom{$-$}$0.183\,883\,70(1)$ & \hphantom{$-$}$5.140\,526(1)\times10^{-4}$ & \hphantom{$-$}0 \\
+    6 & $-0.659\,171\,4(1)$ & \hphantom{$-$}$2.088\,65(1)\times 10^{-4}$ & $-95.168\,96(1)$ \\
+    7 & \hphantom{$-$}$2.937\,665(3)$ & \hphantom{$-$}$4.481\,9(1)\times10^{-5}$ & \hphantom{$-$}0 \\
+    8 & $-15.61(1)$ & \hphantom{$-$}$3.16\times10^{-7}$ & \hphantom{$-$}1457.62(3) \\
+    9 & \hphantom{$-$}96.76 & $-4.31\times10^{-6}$ & \hphantom{$-$}0 \\
+    10 & $-679$ & $-1.99\times10^{-6}$ & $-25\,891(2)$ \\
+    11 & \hphantom{$-$}$5.34\times10^3$ & & \hphantom{$-$}0 \\
+    12 & $-4.66\times10^4$ & & \hphantom{$-$}$5.02\times10^5$ \\
+    13 & \hphantom{$-$}$4.46\times10^5$ & & \hphantom{$-$}0 \\
+    14 & $-4.66\times10^6$ & & $-1.04\times10^7$
   \end{tabular}
+  \caption{
+    Known series coefficients for the universal scaling functions. This with
+    trailing dots are known exactly or have closed integral representations.
+    Those with listed uncertainties are taken from Mangazeev \textit{et al.}\
+    \cite{Mangazeev_2008_Variational}. Those without are taken from Fonseca
+    \textit{et al.}, and are assumed to be accurate to within their last digit
+    \cite{Fonseca_2003_Ising}.
+  }
 \end{table}
 
 \begin{table}
-- 
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