Martín et al. (1992) provides two simple formulas for approximating
to graphical accuracy, one for 
,
the other for 
.
Moshier (1989, §6.14) provides minimax rational approximations
for calculating , 
, 
, 
.
They are in terms of the variable
, where
when 
is positive,
when is negative,
and 
when 
.
The approximations apply when 
, that is,
when 
or 
.
The precision in the coefficients is 21S.
These expansions are for real arguments and are supplied in sets of four
for each function, corresponding to intervals 
,
, 
, 
. The constants 
and
are chosen numerically, with a view to equalizing the effort required for
summing the series.
Razaz and Schonfelder (1980) covers , , ,
. The Chebyshev coefficients are given to 30D.
Corless et al. (1992) describe a method of approximation based on
subdividing 
into a triangular mesh, with values of 
,
stored at the nodes. and are then
computed from Taylor-series expansions centered at one of the nearest nodes.
The Taylor coefficients are generated by recursion, starting from the stored
values of , at the node. Similarly for
, 
.
MacLeod (1994) supplies Chebyshev-series expansions to cover
for and 
for
. The Chebyshev coefficients are given to 20D.
,
,
,
(see also (