Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File


Developed with Mathematica -- Download a Free Trial Version


Mathematica Notation

Traditional Notation

Elliptic Functions > WeierstrassP[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: