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authorJaron Kent-Dobias <jaron@kent-dobias.com>2022-06-04 12:42:32 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2022-06-04 12:42:32 +0200
commitda5391b56d7aacd8c18643f3854358536e01fef9 (patch)
treecaccbcb4e11a6790b7dc34d969ce31d0d26093df
parenta71303cdbc4c30670fb54513fc560d39cf85753f (diff)
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Some work.
-rw-r--r--frsb_kac-rice.tex14
1 files changed, 2 insertions, 12 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 3d06e20..0fa768a 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -279,18 +279,8 @@ and
+\frac12\int_0^1dq\,\left[
\hat\epsilon^2\lambda(q)f''(q)
+\frac1{\lambda(q)+R_d/\hat\epsilon}
- \right]\\
- -\mu R_d-\log\left(\frac1{2f''(1)}\left(\mu\pm\sqrt{\mu^2-4f''(1)}\right)\right)+\frac12\left(1+\frac\mu{2f''(1)}\left(\mu\pm\sqrt{\mu^2-4f''(1)}\right)\right)
+ \right]-\mu R_d+\frac12R_d^2f''(1)+\log R_d\\
+ +\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{align*}
-All that changes is now
-\[
- R_d=\frac12\left(
- (1-q^*)\hat\epsilon\pm\sqrt{
- (1-q^*)\left(
- (1-q^*)\hat\epsilon^2+8/[f'(1)-f'(q^*) - 2\mu/\hat\epsilon]
- \right)
- }
- \right)
-\]
\end{document}