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EllipticF

Usage

EllipticF[ , m] 用来给出第一类椭圆积分  .


Notes

• 数学函数(参见 A.3.10节)
• 对于  ,  .
• 与 EllipticF 相关的完全椭圆积分是 EllipticK.
EllipticFJacobiAmplitude的逆.若  ,则  .
• 沿  到无穷的射线, EllipticF[ , m]有一条不连续分支线.
• 参见3.2.11节对椭圆积分参数约定的讨论.
• 参见Mathematica 全书:3.2.11节.
• 同时参见: JacobiZeta, JacobiAmplitude.
Further Examples

This is the definition of the elliptic integral of the first kind. Classically, the integral is defined for  on the interval  , but the function also makes sense for more general (complex-valued)  .

In[1]:=  

Out[1]=

Setting  gives the complete elliptic integral of the first kind, which is traditionally denoted by a different letter,  .

In[2]:=  

Out[2]=

These are the partial derivatives.

In[3]:=  

Out[3]=

In[4]:=  

Out[4]=