|
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:
|
