From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 20 Oct 2022 18:25:31 +0200
Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

---
 source/know/concept/cauchy-principal-value/index.md | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

(limited to 'source/know/concept/cauchy-principal-value')

diff --git a/source/know/concept/cauchy-principal-value/index.md b/source/know/concept/cauchy-principal-value/index.md
index a2582f2..f09611b 100644
--- a/source/know/concept/cauchy-principal-value/index.md
+++ b/source/know/concept/cauchy-principal-value/index.md
@@ -7,15 +7,15 @@ categories:
 layout: "concept"
 ---
 
-The **Cauchy principal value** $\mathcal{P}$,
+The **Cauchy principal value** $$\mathcal{P}$$,
 or just **principal value**,
 is a method for integrating problematic functions,
 i.e. functions with singularities,
 whose integrals would otherwise diverge.
 
-Consider a function $f(x)$ with a singularity at some finite $x = b$,
+Consider a function $$f(x)$$ with a singularity at some finite $$x = b$$,
 which is hampering attempts at integrating it.
-To resolve this, we define the Cauchy principal value $\mathcal{P}$ as follows:
+To resolve this, we define the Cauchy principal value $$\mathcal{P}$$ as follows:
 
 $$\begin{aligned}
     \boxed{
@@ -24,8 +24,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-If $f(x)$ instead has a singularity at postive infinity $+\infty$,
-then we define $\mathcal{P}$ as follows:
+If $$f(x)$$ instead has a singularity at postive infinity $$+\infty$$,
+then we define $$\mathcal{P}$$ as follows:
 
 $$\begin{aligned}
     \boxed{
@@ -34,10 +34,10 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-And analogously for $-\infty$.
-If $f(x)$ has singularities both at $+\infty$ and at $b$,
+And analogously for $$-\infty$$.
+If $$f(x)$$ has singularities both at $$+\infty$$ and at $$b$$,
 then we simply combine the two previous cases,
-such that $\mathcal{P}$ is given by:
+such that $$\mathcal{P}$$ is given by:
 
 $$\begin{aligned}
     \mathcal{P} \int_{a}^\infty f(x) \:dx
@@ -49,5 +49,5 @@ And so on, until all problematic singularities have been dealt with.
 
 In some situations, for example involving
 the [Sokhotski-Plemelj theorem](/know/concept/sokhotski-plemelj-theorem/),
-the symbol $\mathcal{P}$ is written without an integral,
+the symbol $$\mathcal{P}$$ is written without an integral,
 in which case the calculations are implicitly integrated.
-- 
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