The elliptic exponential function 
gives the value of 
in the elliptic logarithm
 |
for 
and 
real such that 
.
It is implemented in the Wolfram Language as EllipticExp[u,
a,
b
],
which returns 
together with the superfluous parameter 
which multiplies the above integral by
a factor of 
.
The top plot above shows 
(red), 
(violet), and 
(blue) for 
. The other plots show 
in the complex plane.
The plots above show 
in the complex plane for 
.
As can be seen from the plots, the elliptic exponential function is doubly periodic in the complex plane.
