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WeierstrassSigma

  • WeierstrassSigma[ u , , ] gives the Weierstrass sigma function .
  • Mathematical function (see Section A.3.10).
  • Related to WeierstrassZeta by the differential equation .
  • WeierstrassSigma 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: WeierstrassZeta.

    Further Examples

    WeierstrassSigma 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. (We need bignums to get the next example to work.)

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    The Weierstrass sigma function satisfies the following quasi-periodicity condition: if is any element of the lattice generated by the periods and , then for all , where are constants depending on . For , we have and , where is the Weierstrass zeta function. Here is an example, with .

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