The elliptic logarithm is generalization of integrals of the form
 |
for 
real, which can be expressed in terms of logarithmic and inverse trigonometric functions,
to
 |
for 
and 
real. This integral can be done analytically, but has a complicated form involving
incomplete elliptic integrals of the first kind with complex parameters. The plots
above show the special case 
.
The elliptic logarithm is implemented in the Wolfram Language as EllipticLog[
x, y
, 
a, b
], where 
is an unfortunate and superfluous parameter that must be set
to either 
or 
and which multiplies the above integral by a factor of 
.
The inverse of the elliptic logarithm is the elliptic exponential function.
