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.