scipy.special.ellipkm1#
- scipy.special.ellipkm1(p, out=None) = <ufunc 'ellipkm1'>#
- Complete elliptic integral of the first kind around m = 1 - This function is defined as \[\begin{split}K(p) = \\int_0^{\\pi/2} [1 - m \\sin(t)^2]^{-1/2} dt\end{split}\]- where m = 1 - p. - Parameters:
- parray_like
- Defines the parameter of the elliptic integral as m = 1 - p. 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- Kscalar or ndarray
- Value of the elliptic integral. 
 
 - See also - Notes - Wrapper for the Cephes [1] routine ellpk. - For - p <= 1, computation uses the approximation,\[\begin{split}K(p) \\approx P(p) - \\log(p) Q(p),\end{split}\]- where \(P\) and \(Q\) are tenth-order polynomials. The argument p is used internally rather than m so that the logarithmic singularity at - m = 1will be shifted to the origin; this preserves maximum accuracy. For- p > 1, the identity\[\begin{split}K(p) = K(1/p)/\\sqrt(p)\end{split}\]- is used. - References [1]- Cephes Mathematical Functions Library, http://www.netlib.org/cephes/