scipy.special.ellipe¶
- scipy.special.ellipe(m) = <ufunc 'ellipe'>¶
Complete elliptic integral of the second kind
This function is defined as
\[E(m) = \int_0^{\pi/2} [1 - m \sin(t)^2]^{1/2} dt\]Parameters: m : array_like
Defines the parameter of the elliptic integral.
Returns: E : ndarray
Value of the elliptic integral.
See also
Notes
Wrapper for the Cephes [R344] routine ellpe.
For m > 0 the computation uses the approximation,
\[E(m) \approx P(1-m) - (1-m) \log(1-m) Q(1-m),\]where \(P\) and \(Q\) are tenth-order polynomials. For m < 0, the relation
\[E(m) = E(m/(m - 1)) \sqrt(1-m)\]is used.
References
[R344] (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html