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.