Readded expression for D(mu).

1 files changed, 5 insertions, 1 deletions

diff --git a/frsb_kac_new.tex b/frsb_kac_new.tex
index 552ee9b..e1c5768 100644
--- a/frsb_kac_new.tex
+++ b/frsb_kac_new.tex
@@ -295,7 +295,11 @@ Introducing the parameters:
   \begin{aligned}
     \mathcal D(\mu)
     &=\frac1N\overline{\log|\det(\partial\partial H(s_a)+\mu I)|}
-    =\int d\lambda\,\rho(\lambda+\mu)\log|\lambda| 
+    =\int d\lambda\,\rho(\lambda+\mu)\log|\lambda| \\
+    &=\operatorname{Re}\left\{
+    \frac12\left(1+\frac\mu{2f''(1)}\left(\mu\pm\sqrt{\mu^2-4f''(1)}\right)\right)
+    -\log\left(\frac1{2f''(1)}\left(\mu\pm\sqrt{\mu^2-4f''(1)}\right)\right)
+  \right\}
   \end{aligned}
 \end{equation}