--- a/scripts/polynomial/residue.m
+++ b/scripts/polynomial/residue.m
@@ -19,8 +19,10 @@
 
 ## -*- texinfo -*-
 ## @deftypefn {Function File} {[@var{r}, @var{p}, @var{k}, @var{e}] =} residue (@var{b}, @var{a})
-## Compute the partial fraction expansion for the quotient of the
-## polynomials, @var{b} and @var{a}.
+## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k})
+## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k}, @var{e})
+## The first calling form computes the partial fraction expansion for the
+## quotient of the polynomials, @var{b} and @var{a}.
 ## @tex
 ## $$
 ## {B(s)\over A(s)} = \sum_{m=1}^M {r_m\over (s-p_m)^e_m}
@@ -77,12 +79,11 @@
 ##
 ## @end ifnottex
 ##
-## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k})
-## @deftypefnx {Function File} {[@var{b}, @var{a}] =} residue (@var{r}, @var{p}, @var{k}, @var{e})
-## Compute the reconstituted quotient of polynomials,
-## @var{b}(s)/@var{a}(s), from the partial fraction expansion;
-## represented by the residues, poles, and a direct polynomial specified
-## by @var{r}, @var{p} and @var{k}, and the pole multiplicity @var{e}.
+## The second calling form performs the inverse operation and computes
+## the reconstituted quotient of polynomials, @var{b}(s)/@var{a}(s),
+## from the partial fraction expansion; represented by the residues,
+## poles, and a direct polynomial specified by @var{r}, @var{p} and
+## @var{k}, and the pole multiplicity @var{e}.
 ##
 ## If the multiplicity, @var{e}, is not explicitly specified the multiplicity is
 ## determined by the function @code{mpoles}.