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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:
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