The elliptic logarithm is the particular case of the hypergeometric function of two variables (Appell function ):
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 :
The elliptic logarithm is the inverse function to the elliptic exponent and its derivative . Relations between them are described by the following formulas:
