Connections within the group of elliptic exp and elliptic log and with other function groups

Representations through more general functions

The elliptic logarithm is the particular case of the hypergeometric function of two variables (Appell function ):

Representations through related equivalent functions

The elliptic exponent is connected with Jacobi amplitude by the following formula:

The elliptic exponent and elliptic logarithm can be expressed through direct and inverse Weierstrass functions by the following formulas:

The elliptic logarithm has the following representation through incomplete elliptic integral :

Relations to inverse functions

The elliptic logarithm is the inverse function to the elliptic exponent and its derivative . Relations between them are described by the following formulas: