summaryrefslogtreecommitdiff
path: root/content/know/concept/holomorphic-function/index.pdc
diff options
context:
space:
mode:
authorPrefetch2021-03-08 15:04:06 +0100
committerPrefetch2021-03-08 15:04:06 +0100
commit540d23bff03bedbc8f68287d71c8b5e7dc54b054 (patch)
treec3331ad86ea4be57e5c6c8385c9ac75b5dde6227 /content/know/concept/holomorphic-function/index.pdc
parent7bf913f9bc7ab9f8f03c5530d245cf95e1edb43e (diff)
Expand knowledge base
Diffstat (limited to 'content/know/concept/holomorphic-function/index.pdc')
-rw-r--r--content/know/concept/holomorphic-function/index.pdc6
1 files changed, 3 insertions, 3 deletions
diff --git a/content/know/concept/holomorphic-function/index.pdc b/content/know/concept/holomorphic-function/index.pdc
index 3e7a91e..1077060 100644
--- a/content/know/concept/holomorphic-function/index.pdc
+++ b/content/know/concept/holomorphic-function/index.pdc
@@ -196,7 +196,7 @@ $$\begin{aligned}
\end{aligned}$$
**Cauchy's residue theorem** generalizes Cauchy's integral theorem
-to meromorphic functions, and states that the integral of a contour $C$,
+to meromorphic functions, and states that the integral of a contour $C$
depends on the simple poles $p$ it encloses:
$$\begin{aligned}
@@ -206,7 +206,7 @@ $$\begin{aligned}
\end{aligned}$$
*__Proof__*. *From the definition of a meromorphic function,
-we know that we can decompose $f(z)$ as follows,
+we know that we can decompose $f(z)$ like so,
where $h(z)$ is holomorphic and $p$ are all its poles:*
$$\begin{aligned}
@@ -228,5 +228,5 @@ This theorem might not seem very useful,
but in fact, thanks to some clever mathematical magic,
it allows us to evaluate many integrals along the real axis,
most notably [Fourier transforms](/know/concept/fourier-transform/).
-It can also be used to derive the Kramers-Kronig relations.
+It can also be used to derive the [Kramers-Kronig relations](/know/concept/kramers-kronig-relations).