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:
