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WeierstrassSigma

Usage

WeierstrassSigma[u,   ,   ] 给出Weierstrass Sigma 函数


Notes

• 数学函数(参见节A.3.10).
• 由微分方程  描述WeierstrassZeta
WeierstrassSigma不是周期的,因而并不是严格椭圆函数。
• 参见3.2.11节对椭圆函数和相关函数的参数约定的讨论。
• 参见Mathematica 全书: 3.2.11.
• 同时参见: 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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