From e1235c258fe513daab04e0cfe1560d883fd94845 Mon Sep 17 00:00:00 2001
From: Kun Chen <chenkun0228@gmail.com>
Date: Thu, 25 May 2023 10:52:48 -0400
Subject: [PATCH] update docs

---
 docs/src/manual/ladder_3D.md | 2 +-
 src/polarization.jl          | 2 --
 2 files changed, 1 insertion(+), 3 deletions(-)

diff --git a/docs/src/manual/ladder_3D.md b/docs/src/manual/ladder_3D.md
index 70a0c25..f747c06 100644
--- a/docs/src/manual/ladder_3D.md
+++ b/docs/src/manual/ladder_3D.md
@@ -14,7 +14,7 @@ Define ``\vec{k}+\vec{p}=-\vec{p}' `` for the first term, then rename it as ``\v
 \begin{split}
 =&  \int \frac{d^3 \vec{p}}{\left(2\pi^3\right)} \frac{f\left(\frac{p^2}{2 m}-\mu\right)-f\left(-\frac{p^2}{2 m}+\mu\right)}{i \Omega_n-\frac{p^2}{2 m}-\frac{(\vec{p}+\vec{k})^2}{2 m}+2 \mu} \\
 =&  \int \frac{d^3 \vec{p}}{\left(2\pi^3\right)} \frac{2f\left(\frac{p^2}{2 m}-\mu\right)-1}{i \Omega_n-\frac{p^2}{2 m}-\frac{(\vec{p}+\vec{k})^2}{2 m}+2 \mu} \\
-=& -\int \frac{d^3 \vec{p}}{\left(2\pi^3\right)} \frac{1}{i \Omega_n-\frac{p^2}{2 m}-\frac{(\vec{p}+\vec{k})^2}{2 m}+2 \mu} +\int \frac{d^3 \vec{p}}{(2 \pi)^3} \frac{2f\left(\frac{p^2}{2 m}-\mu\right)}{i \Omega_n-\frac{p^2}{2 m}-\frac{\left(\vec{p}+k^2\right)}{2 m}+2 \mu}
+=& -\int \frac{d^3 \vec{p}}{\left(2\pi^3\right)} \frac{1}{i \Omega_n-\frac{p^2}{2 m}-\frac{(\vec{p}+\vec{k})^2}{2 m}+2 \mu} +\int \frac{d^3 \vec{p}}{(2 \pi)^3} \frac{2f\left(\frac{p^2}{2 m}-\mu\right)}{i \Omega_n-\frac{p^2}{2 m}-\frac{\left(\vec{p}+\vec{k}\right)^2}{2 m}+2 \mu}
 \end{split}
 ```
 
diff --git a/src/polarization.jl b/src/polarization.jl
index 81e6c87..cdcaa64 100644
--- a/src/polarization.jl
+++ b/src/polarization.jl
@@ -119,7 +119,6 @@ where we subtract the UV divergent term that is a constant proportional to the U
  - q: momentum
  - n: matsubara frequency given in integer s.t. Ωn=2πTn
  - param: other system parameters
- - maxk: optional, upper limit of integral -> maxk*kF
  - scaleN: optional, N of Log grid in LogDensedGrid, check CompositeGrids for more detail
  - minterval: optional, actual minterval of grid is this value times min(q,kF)
  - gaussN: optional, N of GaussLegendre grid in LogDensedGrid.
@@ -221,7 +220,6 @@ where we subtract the UV divergent term that is a constant proportional to the U
  - q: momentum
  - n: matsubara frequency given in integer s.t. Ωn=2πTn
  - param: other system parameters
- - maxk: optional, upper limit of integral -> maxk*kF
  - scaleN: optional, N of Log grid in LogDensedGrid, check CompositeGrids for more detail
  - minterval: optional, actual minterval of grid is this value times min(q,kF)
  - gaussN: optional, N of GaussLegendre grid in LogDensedGrid.