kugel: Minor corrections

1 files changed, 6 insertions, 6 deletions

diff --git a/buch/papers/kugel/spherical-harmonics.tex b/buch/papers/kugel/spherical-harmonics.tex
index 5a17b99..54c8fa9 100644
--- a/buch/papers/kugel/spherical-harmonics.tex
+++ b/buch/papers/kugel/spherical-harmonics.tex
@@ -607,11 +607,11 @@ short. Let's do for example lemma \ref{kugel:thm:associated-legendre-ortho}.
 \end{proof}
 
 But that was still rather informative and had a bit of explanation, which is
-terrible. Real snobs, such as Wikipedia contributors, some authors and sometimes
-regrettably even ourselves, would write instead:
+terrible. Real snobs, such as Wikipedia contributors, some authors and
+regrettably sometimes even ourselves, would write instead:
 
 \begin{proof}[
-    Pretentiously short proof of lemma \ref{kugel:thm:associated-legendre-ortho}
+    Infuriatingly short proof of lemma \ref{kugel:thm:associated-legendre-ortho}
   ]
   The associated Legendre polynomials are solutions of the associated Legendre
   equation which is a Sturm-Liouville problem and are thus orthogonal to each
@@ -688,9 +688,9 @@ In some other branches of physics such as seismology and quantum mechanics there
 is a so called Condon-Shortley phase factor $(-1)^m$ in front of the square root
 in the definition of the normalized spherical harmonics. It is yet another
 normalization that is added for physical reasons that are not very relevant to
-our discussion, but mention its existence this potential source of confusion
-since many numerical packages (such as \texttt{SHTOOLS} \kugeltodo{Reference})
-offer an option to add or remove it from the computation.
+our discussion, but we mention this potential source of confusion since many
+numerical packages (such as \texttt{SHTOOLS} \kugeltodo{Reference}) offer an
+option to add or remove it from the computation.
 
 Though, for our purposes we will mostly only need the orthonormal spherical
 harmonics, so from now on, unless specified otherwise when we say spherical