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Diffstat (limited to 'content/know/concept/holomorphic-function/index.pdc')
| -rw-r--r-- | content/know/concept/holomorphic-function/index.pdc | 6 |
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). |