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variants of this functions
InverseWeierstrassP






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Elliptic Functions > InverseWeierstrassP[z,{g2,g3}] > Introduction to the Weierstrass functions and inverses





Connections within the group of Weierstrass functions and inverses and with other function groups


The Weierstrass elliptic function and its inverse can be represented through the more general hypergeometric Appell function of two variables by the following formulas:

The Weierstrass functions , , , , , , and can be represented through some related equivalent functions, for example, through Jacobi functions:

where is modular lambda function, or through theta functions:

or through elliptic integrals and the inverse elliptic nome:

The Weierstrass function and its derivative are interconnected with the inverse functions and by the following formulas:

Each of the Weierstrass functions , , , , and can be expressed through the other Weierstrass functions using numerous formulas, for example:

Note that the Weierstrass functions , , , , and form a chain with respect to differentiation:





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