--- a/libinterp/corefcn/ellipj.cc	Wed Sep 04 08:20:25 2013 -0700
+++ b/libinterp/corefcn/ellipj.cc	Wed Sep 04 10:13:53 2013 -0700
@@ -146,13 +146,14 @@
 If @var{u} is a column vector and @var{m} is a row vector, the\n\
 results are matrices with @code{length (@var{u})} rows and\n\
 @code{length (@var{m})} columns.  Otherwise, @var{u} and\n\
-@var{m} must conform and the results will be the same size.\n\
+@var{m} must conform in size and the results will be the same size as the\n\
+inputs.\n\
 \n\
 The value of @var{u} may be complex.\n\
-The value of @var{m} must be 0 @leq{} m @leq{} 1.\n\
+The value of @var{m} must be 0 @leq{} @var{m} @leq{} 1.\n\
 \n\
-@var{tol} is currently ignored (@sc{matlab} uses this to allow faster,\n\
-less accurate approximation).\n\
+The optinoal input @var{tol} is currently ignored (@sc{matlab} uses this to\n\
+allow faster, less accurate approximation).\n\
 \n\
 If requested, @var{err} contains the following status information\n\
 and is the same size as the result.\n\
@@ -165,9 +166,11 @@
 Error---no computation, algorithm termination condition not met,\n\
 return @code{NaN}.\n\
 @end enumerate\n\
- Ref: Abramowitz, Milton and Stegun, Irene A\n\
-      Handbook of Mathematical Functions, Dover, 1965\n\
-      Chapter 16 (Sections 16.4, 16.13 and 16.15)\n\
+\n\
+Reference: Milton Abramowitz and Irene A Stegun,\n\
+@cite{Handbook of Mathematical Functions}, Chapter 16 (Sections 16.4, 16.13,\n\
+and 16.15), Dover, 1965.\n\
+\n\
 @seealso{ellipke}\n\
 @end deftypefn")
 {

--- a/scripts/specfun/ellipke.m	Wed Sep 04 08:20:25 2013 -0700
+++ b/scripts/specfun/ellipke.m	Wed Sep 04 10:13:53 2013 -0700
@@ -19,19 +19,22 @@
 ## <http://www.gnu.org/licenses/>.
 
 ## -*- texinfo -*-
-## @deftypefn  {Function File} {} ellipke (@var{m})
-## @deftypefnx {Function File} {} ellipke (@var{m}, @var{tol})
+## @deftypefn  {Function File} {@var{k} =} ellipke (@var{m})
+## @deftypefnx {Function File} {@var{k} =} ellipke (@var{m}, @var{tol})
 ## @deftypefnx {Function File} {[@var{k}, @var{e}] =} ellipke (@dots{})
-## Compute complete elliptic integral of the first K(@var{m}) and second
+## Compute complete elliptic integrals of the first K(@var{m}) and second
 ## E(@var{m}) kind.
 ##
-## @var{m} is either real array or scalar with 0 @leq{} m @leq{} 1.
+## @var{m} must be a scalar or real array with 0 @leq{} @var{m} @leq{} 1.
+##
+## The optional input @var{tol} is currently ignored (@sc{matlab} uses this
+## to allow a faster, less accurate approximation).
 ##
-## @var{tol} is currently ignored (@sc{matlab} uses this to allow faster,
-## less accurate approximation).
+## Called with only one output, elliptic integrals of the first kind are
+## returned.
 ##
-## Ref: Abramowitz, Milton and Stegun, Irene A. Handbook of Mathematical
-## Functions, Dover, 1965, Chapter 17.
+## Reference: Milton Abramowitz and Irene A. Stegun,
+## @cite{Handbook of Mathematical Functions}, Chapter 17, Dover, 1965.
 ## @seealso{ellipj}
 ## @end deftypefn