mars.tensor.special.ellipkm1#
- mars.tensor.special.ellipkm1(x, **kwargs)[源代码]#
Complete elliptic integral of the first kind around m = 1
This function is defined as
\[K(p) = \int_0^{\pi/2} [1 - m \sin(t)^2]^{-1/2} dt\]where m = 1 - p.
- 参数
p (array_like) – Defines the parameter of the elliptic integral as m = 1 - p.
- 返回
K – Value of the elliptic integral.
- 返回类型
ndarray
备注
Wrapper for the Cephes 1 routine ellpk.
For p <= 1, computation uses the approximation,
\[K(p) \approx P(p) - \log(p) Q(p),\]where \(P\) and \(Q\) are tenth-order polynomials. The argument p is used internally rather than m so that the logarithmic singularity at m = 1 will be shifted to the origin; this preserves maximum accuracy. For p > 1, the identity
\[K(p) = K(1/p)/\sqrt(p)\]is used.
参见
引用
- 1
Cephes Mathematical Functions Library, http://www.netlib.org/cephes/