--- a/scripts/specfun/nchoosek.m
+++ b/scripts/specfun/nchoosek.m
@@ -21,7 +21,8 @@
 ## @deftypefn  {Function File} {@var{c} =} nchoosek (@var{n}, @var{k})
 ## @deftypefnx {Function File} {@var{c} =} nchoosek (@var{set}, @var{k})
 ##
-## Compute the binomial coefficient or all combinations of a set of items.
+## Compute the binomial coefficient of @var{n} or list all possible
+## combinations of a @var{set} of items.
 ##
 ## If @var{n} is a scalar then calculate the binomial coefficient
 ## of @var{n} and @var{k} which is defined as
@@ -75,10 +76,10 @@
 ## @end group
 ## @end example
 ##
-## @code{nchoosek} works only for non-negative, integer arguments.  Use
-## @code{bincoeff} for non-integer and negative scalar arguments, or for
-## computing many binomial coefficients at once with vector inputs
-## for @var{n} or @var{k}.
+## Programming Note: When calculating the binomial coefficient @code{nchoosek}
+## works only for non-negative, integer arguments.  Use @code{bincoeff} for
+## non-integer and negative scalar arguments, or for computing many binomial
+## coefficients at once with vector inputs for @var{n} or @var{k}.
 ##
 ## @seealso{bincoeff, perms}
 ## @end deftypefn
@@ -87,16 +88,17 @@
 ## Author: Paul Kienzle <pkienzle@users.sf.net>
 ## Author: Jaroslav Hajek
 
-function A = nchoosek (v, k)
+function C = nchoosek (v, k)
 
   if (nargin != 2
-      || !isnumeric (k) || !isnumeric (v)
-      || !isscalar (k) || ! (isscalar (v) || isvector (v)))
+      || ! (isreal (k) && isscalar (k))
+      || ! (isnumeric (v) && isvector (v)))
     print_usage ();
   endif
-  if (k < 0 || k != fix (k)
-      || (isscalar (v) && (v < k || v < 0 || v != fix (v))))
-    error ("nchoosek: args are non-negative integers with V not less than K");
+  if (k < 0 || k != fix (k))
+    error ("nchoosek: K must be an integer >= 0");
+  elseif (isscalar (v) && (iscomplex (v) || v < k || v < 0 || v != fix (v)))
+    error ("nchoosek: N must be a non-negative integer >= K");
   endif
 
   n = length (v);
@@ -104,39 +106,39 @@
   if (n == 1)
     ## Improve precision at next step.
     k = min (k, v-k);
-    A = round (prod ((v-k+1:v)./(1:k)));
-    if (A*2*k*eps >= 0.5)
-      warning ("nchoosek", "nchoosek: possible loss of precision");
+    C = round (prod ((v-k+1:v)./(1:k)));
+    if (C*2*k*eps >= 0.5)
+      warning ("nchoosek: possible loss of precision");
     endif
   elseif (k == 0)
-    A = zeros (1,0);
+    C = zeros (1,0);
   elseif (k == 1)
-    A = v(:);
+    C = v(:);
   elseif (k == n)
-    A = v(:).';
+    C = v(:).';
   elseif (k > n)
-    A = zeros (0, k, class (v));
+    C = zeros (0, k, class (v));
   elseif (k == 2)
     ## Can do it without transpose.
     x = repelems (v(1:n-1), [1:n-1; n-1:-1:1]).';
     y = cat (1, cellslices (v(:), 2:n, n*ones (1, n-1)){:});
-    A = [x, y];
+    C = [x, y];
   elseif (k < n)
     v = v(:).';
-    A = v(k:n);
+    C = v(k:n);
     l = 1:n-k+1;
     for j = 2:k
-      c = columns (A);
-      cA = cellslices (A, l, c*ones (1, n-k+1), 2);
+      c = columns (C);
+      cA = cellslices (C, l, c*ones (1, n-k+1), 2);
       l = c-l+1;
       b = repelems (v(k-j+1:n-j+1), [1:n-k+1; l]);
-      A = [b; cA{:}];
+      C = [b; cA{:}];
       l = cumsum (l);
       l = [1, 1 + l(1:n-k)];
     endfor
-    clear cA b;
-    A = A.';
+    C = C.';
   endif
+
 endfunction
 
 
@@ -145,14 +147,19 @@
 %!assert (size (nchoosek (1:5,0)), [1 0])
 
 %% Test input validation
-%!warning nchoosek (100,45);
+%!error nchoosek ()
+%!error nchoosek (1)
+%!error nchoosek (1,2,3)
+
+%!error nchoosek (100, 2i)
+%!error nchoosek (100, [2 3])
 %!error nchoosek ("100", 45)
-%!error nchoosek (100, "45")
-%!error nchoosek (100, ones (2,2))
-%!error nchoosek (repmat (100, [2 2]), 45)
-%!error nchoosek (100, -45)
-%!error nchoosek (100, 45.5)
-%!error nchoosek (100, 145)
-%!error nchoosek (-100, 45)
-%!error nchoosek (100.5, 45)
+%!error nchoosek (100*ones (2, 2), 45)
+%!error <K must be an integer .= 0> nchoosek (100, -45)
+%!error <K must be an integer .= 0> nchoosek (100, 45.5)
+%!error <N must be a non-negative integer .= K> nchoosek (100i, 2)
+%!error <N must be a non-negative integer .= K> nchoosek (100, 145)
+%!error <N must be a non-negative integer .= K> nchoosek (-100, 45)
+%!error <N must be a non-negative integer .= K> nchoosek (100.5, 45)
+%!warning <possible loss of precision> nchoosek (100, 45);