Update 9 for #331.

doc/sphinx/src/models.rst

@@ -793,7 +793,7 @@ thermodynamic derivatives we can show that
 
     \Gamma \rho = \frac{\alpha B_T}{C_V} ,
 
-and we arrive at
+and we arrive at 
 
 .. math::
 
@@ -814,8 +814,9 @@ The pressure, energy, and temperature, on the Hugoniot are derived from the
 shock jump conditions,
 
 .. math::
-  \rho_0 U_s = \rho (U_s - u_p) \\
-  P_H = \rho_0 U_s u_p \ , \ \ \ \         
+
+  \rho_0 U_s &= \rho (U_s - u_p) \\
+  P_H &= \rho_0 U_s u_p \ , 
 
 assuming a linear :math:`U_s`- :math:`u_p` relation,
 
@@ -859,10 +860,11 @@ we can solve
 into the explicit formula
 
 .. math::
-      T_H(\rho) = T_0 e^{\Gamma(\rho_0) \eta} + \frac{C_s^2}{2 C_V s^2} 
+
+      T_H(\rho) &= T_0 e^{\Gamma(\rho_0) \eta} + \frac{C_s^2}{2 C_V s^2} 
                 \left[\frac{- s \eta}{(1 - s \eta)^2} + \left( \frac{\Gamma(\rho_0)}{s} - 3 \right) 
-                                        \left( e^{\Gamma(\rho_0) \eta} - \frac{1}{(1-s \eta)}\right) \\
-      \ \ \ \ \ \ \  + e^{-\frac{\Gamma(\rho_0)}{s} (1-s \eta)} 
+                                        \left( e^{\Gamma(\rho_0) \eta} - \frac{1}{(1-s \eta)}\right)\right. \\
+           & \ \left. + e^{-\frac{\Gamma(\rho_0)}{s} (1-s \eta)} 
                         \left( Ei(\frac{\Gamma(\rho_0)}{s}(1-s \eta))-Ei(\frac{\Gamma(\rho_0)}{s}) \right)
                         \left((\frac{\Gamma(\rho_0)}{s})^2 - 4 \frac{\Gamma(\rho_0)}{s} + 2 \right) \right]                        
 
@@ -871,7 +873,9 @@ giving an error less than machine precision. For :math:`s \eta` close to :math:`
 severe cancellations in this formula and we use the expansion
 
 .. math::
-    {T_H}_{exp}(\rho) = \ .
+
+    {T_H}_{exp}(\rho) = T_0 e^{\Gamma(\rho_0) \eta} + \frac{C_s^2}{2 C_V s^2} 
+                          \left[ -2 \ln ( 1- s \eta) + \frac{s \eta}{(1 - s \eta)^2} ( 3 s \eta - 2) \ .
 
 
 The constructor for the ``MGUsup`` EOS has the signature