diff --git a/signed_cylinder_marked_polygons_v2.txt b/signed_cylinder_marked_polygons_v2.txt
index 559ea11..715c9e5 100644
--- a/signed_cylinder_marked_polygons_v2.txt
+++ b/signed_cylinder_marked_polygons_v2.txt
@@ -916,16 +916,16 @@ real line with B_0(w) > 0, C(w) > 0 for w > 0, and both are the ratios of an
 odd kernel to its own divided-difference normalisation. Their derivative
 transforms are
 
-    hat{B_0'}(k) = 8k cosh k / sinh 4k,     hat{C'}(k) = 6k / sinh 3k,
+    B_0'(k) = 8k cosh k / sinh 4k,     C'(k) = 6k / sinh 3k,
 
 using hat h(k) = int_R e^{-ikw} h(w) dw. Both densities are strictly positive
 and even, all moments are finite, and
 
-    hat{B_0'}(k) / hat{C'}(k) = (2/3) e^{phi(k)},
+    B_0'(k) / C'(k) = (2/3) e^{phi(k)},
     phi(k) = log((1+t^2)(1-t^6)/(1-t^8)),   t = e^{-|k|},
 
 continued by phi(0) = log(3/2). The identity follows from
-hat{tilde B_beta'}(xi) = 2 pi xi cosh(beta xi) / sinh(pi xi), obtained by
+tilde B_beta'(xi) = 2 pi xi cosh(beta xi) / sinh(pi xi), obtained by
 applying cos beta + sin beta partial_beta to the transform
 int_R e^{i xi t} dt / (cosh t + cos beta) = 2 pi / (sinh(pi xi/2)) times
 the corresponding factor, and then scaling.