This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
 Documentation / Mathematica / Built-in Functions / New in Version 3.0 / Mathematical Functions  /
WeierstrassZeta

  • WeierstrassZeta[ u , , ] gives the Weierstrass zeta function .
  • Mathematical function (see Section A.3.10).
  • Related to WeierstrassP by the differential equation .
  • WeierstrassZeta is not periodic and is therefore not strictly an elliptic function.
  • See Section 3.2.11 for a discussion of argument conventions for elliptic and related functions.
  • See the Mathematica book: Section 3.2.11.
  • See also: WeierstrassSigma.

    Further Examples

    WeierstrassZeta takes as a second argument the coefficients of the equation of the elliptic curve under consideration (in Weierstrass normal form). If instead we know the periods of the curve, we start by using WeierstrassInvariants.

    In[1]:=

    Out[1]=

    The Weierstrass zeta function satisfies the following quasiperiodicity condition: if is any element of the lattice generated by the periods and , then for all , where is a constant depending on . For , we have . Here is an example, with :

    In[2]:=

    Out[2]=

    This is the defining differential equation.

    In[3]:=

    Out[3]=

    This is the integral.

    In[4]:=

    Out[4]=